Consider :

This page contains 12 pages of 50 questions.

Answer all the questions.

Write your index number in the place provided.

For the questions from 1 to 50 select the correct or the most appropriate answer among the answers numbered

(1)> (2)> (3)> (4)> (5) and make a cross(X) in the crossing sheet according to the instructions given.

1. The physical quantity having the unit same as the ratio between the electric flux density and magnetic flux density

B

E is,

(1)Velocity (2)Charge (3)Electric potential (4)Acceleration (5)Force

2. The graphs indicating the distribution of intensity (I)of a black body when

the absolute temperature of its surface is 4T, 5T are shown. If λ1 =10 μm,

then λ2 is,

(1) 4μm (2) 8μm (3) 12μm

(4) 16μm (5) 64μm

3. Which structure correctly shows the change in structure of quarks of nucleon in nucleus and lepton emission during

β-emission of a radioactive element?

4. The wave in a stretched rope has frequency f, and wavelength . When tension of the rope is changed, the frequency

and wavelength of the wave are 3f and 2 respectively. What is the ratio between the initial and final tensions in

the rope?

36

1)1(

6

1)2(

5

1)3( 5)4( 6)5(

λ

I

λ1 λ2

4T

5T

β-

ve

u d d

u d u

(1) n

p

β-

ve

u d d

u d u

(2) p

n

β-

ve

u d u

u d d

(3) p

n

β+

d u u

d u d

(4) p

n

ve

β+

d u u

d u d

(5) n

p

ve

Do not use calculator

(g = 10 N kg-1

)

AL/2020/01/E-I - 1 -

[See page two

5. What is the approximate work done by a cell in order to move 6.28 x1018

electrons across 20V potential difference?

(Charge of an electron is -1.6x10-19

C)

(1) 5J (2) 10J (3) 15J (4) 20J (5) 25J

6. During a thermodynamic process, 2 mol of gas releases 30J of heat energy and 22J of work is done on the gas. If its

initial internal energy is 20J, what is the final internal energy of the gas system?

(1) 72J (2) 32J (3) 28J (4) 12J (5) 8J

7. The sound intensity level at a certain distance from a sound source is 8dB. If the power of the sound source is

increased to 10 times, the sound intensity level at the same point is,

(1) 80dB (2) 0.8dB (3) 7dB (4) 9dB (5) 18dB

8. A steel plate contains a circular hole. The temperature of the plate is increased to 1000C. At that time if the

fractional increase in the area of the hole is 2.4 x 10-3

, what is the co-efficient of linear expansion of that substance

by which the plate is made of?

(1) 2.4 x 10-50

C

(2)1.2 x 10-5 0

C (3) 1.2 x 10-40

C (4) 1.2 x 10-3 0

C

(5) 1.2 x 10-60

C

9. In the given electrical circuit, the currents

through the resistance R1 ,R3 inbetween the

current supply across the x, y ends are 3A,2A

respectively. What is the resultant resistance of

the unknown resistances connected across A, B?

(1) 2Ώ (2) 4Ώ;

(3) 6Ώ (4) 8Ώ (5) 12Ώ

10. A ball is thrown towards the floor from height h. When it rebounds after colliding with the floor, it looses half of its

kinetic energy.Then it reaches a maximum height of 2h before it reaches the floor again.What is the initial speed of

the ball?

gh)1( gh2)2( gh3)3( gh4)4( gh6)5(

11. A one end closed resonance tube P1 is vibrating in its first overtone. Another resonance tube P2 open at both ends is

vibrating in its third overtone. These both frequencies resonate with a particular tuning fork. What is the ratio

between the lengths of the tubes P1, P2?

(1) 8:3 (2) 3:8 (3) 1:2 (4) 1:3 (5) 1:4

12. Two identical masses are connected by an elastic string similar to a spring of force constant k and

unstretched length l. Those 2 masses are hung from the ends of a string which passes over a frictionless

pulley. What is the total length of the string at equilibrium?

k

mg)1(

k

mgl )2(

k

mgl

2)3(

k

mgl

2)4(

k

mgl

3

2)5(

13. Activity of a radiating sample S1 is A0. The number of radioactive nuclei in that sample is twice than that of sample

S2 with activity 2A0. What is the ratio between the half life times of S1 ,S2?

4

1)1(

2

1)2( 1)3( 2)4(

4)5(

x y

R3=6Ώ

R1=4Ώ

R2=8Ώ

R4=3Ώ

R5

R6

R7

R8

2A

3A A B

m m

AL/2020/01/E-I - 2 -

[See page three

14. Eye ring is the appropriate position to keep the eye when observing through an astronomical telescope. In which of

the following, the magnitude of the aperture of eye ring does not depend?

(1) Size of front-most part of objective lens.

(2) Size of front-most part of eyepiece.

(3) Focal length of objective.

(4) Focal length of eye piece.

(5) Distance of the object.

15. Which of the following is/are true regarding current electricity?

(A) When a constant current flow is in a conductor, no any net electric force act on the moving electrons.

(B) In a particular conductor, the work that should be done inorder to move certain amount of charge from one

end to another end across a conductor is a constant.

(C) Electrical pressure is the electric potential.

(1) (A) only (2) (B)only (3) (B), (C)only (4) (A), (B)only (5) All (A), (B), (C)

16. Which of the following ray diagram correctly shows a convex lens acting as a magnifying glass?

17. What is the current through the cell, if the internal

resistance of the cell in the circuit can be neglected?

R

E

11

6)1(

R

E

4

3)2(

R

E

6)3(

R

E

5

3)4(

R

E)5(

18. The figure shows a conical pendulum of length d performing horizontal circular

oscillation with radius r. If the angular frequency of the motion is ɷ, the value of

ɷ2 is,

d

g)1(

r

g)2(

22)3(

rd

g

2 2(4)

g

d r dr

g)5(

R

E

R R

R R

F F

Object

Image

(2)

F F

Object

Image

(4)

F F

Object

Image

(3)

(5)

F F

Object

Image

(1)

F F

Object

Image

r

d

ω

AL/2020/01/E-I - 3 -

[See page four

19. Ice cube of mass m1 which is at 00C is mixed with the water of mass m2 at 100

0C. Which of the following lengths of

thick line correctly shows the values that can be taken for m1 and m2 such that the final mixture contains only water

at final temperature 00C?

20. The refractive index of the glass block ABCD shown in figure is n. A

liquid is pasted on the side AD of the block. A light ray which

incidents on AB at point E enters the block and incidents on the side

AD and grazes along AD. What is the refractive index of the liquid?

1)1( 2 n 1)2( 2 nn

n 1)3(

1)4(

2

2

n

n2

2 1)5(

n

n

21. In the circuit given, the internal resistances of the electric cells of emf E0 and E1

can be neglected. If there is no current flow through the cell of emf E1, the ratio

E1/E0is,

` 3

1)1(

2

1)2(

3

2)3(

2

3)4(

2)5(

22. The nearby graph shows the variation of electric potential V in a

region with the distance d along a straight line.In which of the

point/s on the straight line, the magnitude of electric force acting

along the straight line on a point charge will be maximum?

(1) At P and Q (2) Only atT

(3) At R and T (4) At P and T (5) At R, S and T

23. An electric bulb of 40W is connected in series with a room heater which is under major electric supply. If that

electric bulb is substituted by another electric bulb of 100W, which of the following is true regarding the activity of

heater?

(1)Output remains unchanged. (2)Output will decrease. (3) Output will increase.

(4)Heater does not work. (5)When heater works, it has same resistance at both instances.

24. The maximum tensile stress that can be withstand by unit area of a substance without affecting that substance is

called as tensile strength. The tensile stress of a steel is 415MPa. What is the maximum mass that can be hung from

a vertical, massless steel rod of diameter 2cm?

(1) 1300kg (2) 5200kg (3) 13000kg (4) 52000kg

(5)Depends on the length of steel rod.

m2

m1

(1) (2) (3) (4) (5)

B

E

A

C

D

R

R

R

R E0

E1

d

V

P Q R S T

AL/2020/01/E-I - 4 -

[See page five

25. A point mass is pasted at an unknown position of a narrow mass lessvacuum tube of length

L. Rod is allowed to perform small oscillations of period T about a frictionless horizontal

axis at one end of a rod. Similarly, when the rod is allowed to oscillate about the other

end, the oscillation period is 2T. What is the distance to the point mass from the centre?

8)1(

L

4)2(

L

5

2)3(

L

6)4(

L

10

3)5(

L

26. The frequency of wave emitted from a radar instrument is 750MHz. When this wave is incident on an aeroplane and

reflect back, its frequency seemed to be increased by 2.5kHz when observed from a radar station. What is the speed

of aeroplane towards the radar station? (Velocity of light in air is 3 x108ms

-1)

(1) 4kms-1 (2) 2kms-1 (3) 1kms-1 (4) 0.5kms-1 (5) 0.25kms-1

27.

A block of mass m is connected to a light string. String is passed over the mass less pulley and its other end is

attatched to a fixed point. The horizontal part of the string is of length L. Now another small mass m is hung from

the horizontal part of the string using a ring which can slide on the string. System reaches equilibrium. Neglect

friction at all places. The tension in the fixed end of the string is,

2)1(

mgmg)2(

2

3)3(

mgmg2)4( mg3)5(

28. When a uniform electric field strength of E is passing across a

Gaussian surface of radius r and length L perpendicular to the axis of

the surface, what is the electric flux due to the electric field lines

entering this region?

Er2)1( Er

22)2( rLE)3(

rLE2)4( rLE2)5(

29. The loss in surface energy due to combination of two identical and roughly spherical water drops which are on a

particular surface is converted into the upward kinetic energy of the formed droplet. Due to this energy, the formed

droplet involves to jumping. If this energy transformation is considered to be 100% efficient, what is the

relationship between the radius of the initial water drop r and the maximum jumping height h?

rh)1( 21

)2( rh 21

)3(

rh 1)4( rh 2)5( rh

Fulcrum

r

L

E

AL/2020/01/E-I - 5 -

[See page six

30. The figure shows an equal length of dry air trapped by different lengths of mercury columns in the quill tubes.

Which graph correctly gives the variation of length of trapped air column (l) with temperature (θ) when

temperature is increased?

31. A large block of mass 5kg is moving towards right with the velocity of 10ms-1

. At a particular instance, for every

1m interval from the block of mass 5kg, small blocks of mass 1kg which are initially kept at rest are positioned. All

collisions are inelastic. Neglect the friction. What is the distance that can be travelled by the large block before its

velocity decreases below 3ms-1?

(1) 5m (2) 11m (3) 12m (4) 16m (5) 17m

32.

Person having long-sightedness observes a book at a distance of 25cm from the eye. He could not observe the book

clearly. At this time, the focal point of the eye lens is at A. If he observes clearly by wearing a suitable lens, what is

the type of that lens and the focal point of the combination lens, if the eye lens and the wearing lens are considered

as a combination lens?

(1) Convex lens, B (2) Concave lens, B (3) Convex lens, C

(4) Concave lens,D (5) Convex lens, D

33. In the shown potentiometer circuit, the internal resistance of the electric cell (E)

is negligibly small. The resistance of the potentiometer wire is R. The balance

length obtained for balancing the cell E0 in the potentiometer is l. What is the

change that should be done on the potentiometer in order to change the balance

length as 2l?

(1) Join the resistance R/2 in series with the potentiometer wire.

(2) Join the resistance R in series with the potentiometer wire.

(3) Join the resistance 2R in series with the potentiometer wire.

(4) Instead of cell E, use another cell having emf twice than that of cell E.

(5) Instead of cell E, use another cell with internal resistance and having emf half that of cell E.

A 25cm B C E

O

D

(5) 𝜃

l

A B

0 0

0 0

(3) 𝜃

l A

B

l

0 0

(2) 𝜃

B

A

0 0

(1) 𝜃

l A

B

0 0

(4) 𝜃

l A

B

E

E0

G

l

B A

AL/2020/01/E-I - 6 -

[See page seven

34. An escalator can lift the passengers upwards upto a vertical height of 10m within 30s. A childish person of mass

50kg walks downwards in an escalator which is moving up. Because of that if he is seemed to be at rest with respect

to the building, and if he did this for 30s, what is the total work done by him on the escalator respect to the

building?

J410)1( J

3105)2( J0)3( J3105)4( J

410)5(

35. A planet is revolving around the star at a circular path of radius r0. The star looses its 1% of mass slowly and

uniformly within a very long time than its orbiting period. In this continuous process, if it is assumed that the new

orbit of the planet is taken as circle, the approximate radius of the new orbit is?

(1) 1.02 ro (2) 1.01 ro (3) ro (4) 0.99ro (5) 0.98ro

36. As shown in the figure, blocks P, Q and R of identical masses are

kept on light and frictionless pistons and the system is maintained

at equilibrium. (The amount of fluid is drawn according to the

scale) Initially the valves at points A, B are kept closed.

(1) Among the two valves, when any one of them is opened,

there is no change in the heights of blocks.

(2) Among the two valves, when only A is opened, block P will rise up while block Q moves down.

(3) Among the two valves when any one of them is opened, Q will move down.

(4) When both valves are opened, block Q rises up and blocks P, R will move down.

(5) Among the two valves when only B is opened, block R will rise up and block Q will move down.

37.

A lens of focal length f1 kept at A having XY as its principal axis forms an image at point B with magnification m1

for an object at O1. Likewise, another lens of focal length f2 kept at A having XY as its principal axis forms an

image at point B with magnification m2 for an object at O2. Which of the following is/are true?

(A) Both lenses used are convex.

(B) f2<f1

(C) m1<m2

(1) (A) only. (2) (B) only. (3) (C) only. (4) (A), (B) only (5) All (A), (B), (C)

38.

A constant force F is acting on a frictionless piston of area of cross section A. Density of water is ρand viscous force

can be neglected. What is the time taken to expel water completely through the hole of area of cross section a?

B A

P Q R

X Y O1

A B

O2

A

F

a L

AL/2020/01/E-I - 7 -

[See page eight

)(

2)1(

22aAA

F

a

L

)(2)2(

22aAF

A

L

a

A

aAF

a

L )()3(

22

F

aAA

a

L

2

)()4(

22 F

aAA

a

L

2

)()5(

22

39. Two blocks each of mass m are kept one over the other. The floor is frictionless.

The co-efficient of static and dynamic friction are μs, μk (μs > μk) respectively.

Initially both blocks are kept at rest. Which graph correctly shows the variation

of acceleration (a) with force (F) when a constant horizontal force (F) is applied

on the block which is at the bottom?

40.

In the given electric circuit, switch K2 is closed for a short period of time and then opened. After this, switch K1 is

closed. V1 is the varying voltage supplied by the battery. Which of the following graph gives the variation of voltage

VA at point A with V1 after switch K1 is closed? (Neglect the internal resistance of both power supplies)

A K1

K2

R

R R

V1 V2

C

V2

F

(1) F

a

(2) F

a

(3) F

a

(4) F

a

F (5)

a

V1

VA

00 5V2

-5V2

5V2

(1)

V1

VA

00 5V2

-5V2

5V2

(2)

V1

VA

00 5V2

-5V2

5V2

(3)

V1

VA

00 5V2

-5V2

5V2

(4)

V1

VA

00 5V2

-5V2

5V2

(5)

AL/2020/01/E-I - 8 -

[See page nine

41. The figure given contains a circuit having high voltage

source. The potential drop across the diode when the

diode is forward biased is V0. In the figure shown, 2N

number of diodes are used. If all diodes are forward

biased, In is

R

V1)1(R

VV 01)2(

R

NVV 01)3(

R

NVV

2)4( 01

R

NVV 01 2)5(

42.

The V-I characteristic curve of zenor diode in the figure is given above. E is the cell having varying emf. Its internal

resistance can be neglected. Which graph correctly gives the variation of potential difference V0 across resistor R

with E?

43. In the digital circuit shown, which of the truth tables correctly gives the output F corresponding to the logic input

values A, B, C?

A B C F A B C F A B C F A B C F A B C F

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0

0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 0

0 1 1 1 0 1 1 0 0 1 1 1 0 1 1 0 0 1 1 0

1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1

1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0

1 1 0 1 1 1 0 1 1 0 1 1 1 1 0 0 1 1 0 0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0

(1) (2) (3) (4) (5)

V0

E

R

V/V

I /mA

-2.3

0 0.7

0

(5)

E

VO

0.7

(4)

E

VO

0.7

(3)

E

VO

2.7

(2)

E

VO

3

(1)

E

VO

3

F

B

C

A

AL/2020/01/E-I - 9 -

[See page ten

44.

Inbetween the horizontal conducting plates X, Y shown in figure, voltage difference V with the polarity shown above

is found. The gap between these plates is d. The charge q of mass m shown is moving horizontally with uniform

velocity u along the path shown. Uniform magnetic field B is present perpendicularly into the sheet. Which of the

following relationships is true?

qBud

Vmg

)1( qBu

d

Vmg

)2( qBuVdmg )3(

qd

B

d

Vmg

)4(

Vd

Bqumg )5(

45.

A viscous fluid is found in-between the horizontal parallel surfaces shown in figure. A small thin plate P is placed in

the centre of the surfaces as shown. Initially surfaces, liquid and plate remain at rest. Then as shown in the figure,

while the bottom surface remains at rest, upper surface and plate are moving towards right with velocities V2,V1

respectively as shown. Which of the following statements is true regarding the direction of net viscous frictional

force acting on the plate?

(1) Always towards left.

(2) If V1=V2, no any viscous frictional force act.

(3) If V1=2V2, no any viscous frictional force act.

(4) If 2V1=V2, no any viscous frictional force act.

(5) If V1=0, no any viscous frictional force act.

46.

Combination rod made using 4 rods has the above shown dimensions and thermal conductivities (K) corresponding

to distance (x) indicated in the graph. When the ends of combination rod is kept at constant temperatures as shown,

the temperature difference across the ends of each rod is indicated across the ends of each rod. Which of the

following relationships is true?

4321)1( 3214)2( 3241)3(

4321)4( 3241)5(

Y

V

+ + +

X

q

U

- - - B

m d

V2

V1

P

00C 100

0C

2l 2l 3l l

θ1 θ2 θ3 θ4

x

K

K0

2K0

3K0

00

2l 4l 7l 8l

AL/2020/01/E-I - 10 -

[See page eleven

47. During “Zero-g” flight travel, passengers can feel weightless and

float around a separated room for a certain period of time

duration. The above graph shows the path of that flight travel and

some points denoted in that path. Which of the following

statements is true?

(1) During the motion of flight from time a to c, flight travels

in the upwards direction with the acceleration equal to the

magnitude of gravitational acceleration.

(2) During the motion of flight from time a to c, flight travels with zero acceleration.

(3) During the motion of flight from time b to d, flight travels in the downward direction with the acceleration

equal to the magnitude of gravitational acceleration.

(4) During the motion of flight from time c to e, flight travels in the downward direction with the acceleration

equal to the magnitude of gravitational acceleration.

(5) During the motion of flight from time d to e, flight travels in the downward direction with the acceleration

equal tothe magnitude of gravitational acceleration.

48. A girl with moment of inertia I is dancing on a smooth floor and rotates quickly with the angular velocity ɷ. That

dancer holds a pen of mass m at a distance of R from her rotating axis. Then she drops her pen. After that what

could happen for the vertical component of the angular momentum of the system containing the dancer and pen?

Neglect all the frictions. But, gravitational and other normal forces cannot be neglected.

(1) It will decrease until pen reaches the floor.

(2) It will increase until pen reaches the floor.

(3) It will not change.

(4) It does not change initially but will decrease when the pen reaches the floor.

(5) It does not change initially but will increase when the pen reaches the floor.

49.

Rooms A, B, C of equal volume which are kept under atmospheric pressure and room temperature are found with

relative humidities x%, y%, z% respectively. The absolute humidity of room B is S. (See figure (P)). As shown in

figure (Q), when the doors are opened and the air in three rooms is allowed to get mixed, the common relative

humidity of the three rooms is y%. What is the additional mass of water vapour required to be added in order to

saturate these three rooms with vapour at this temperature?

1

1003)1(

yVS

1

300)2(

yVS

1

300)3(

zyxVS

1

1003)4(

zyxVS

1

300)5(

yzxVS

Time

Height

a b c d e

A B C

(Q) (P)

S

A B C

x% y% z%

AL/2020/01/E-I - 11 -

[See page twelve

50. Circular conductor A is held horizontally and stationarily as shown in the figure. A

small strong bar magnet is dropped along the axis of conductor. Which of the

following graph is the possible representation of the variation of its acceleration (a)

with time (t) in its following motion?

N

S

A

(5) t

a

0 0

(1) t

a

0 0

(2) t

a

0 0

(3) t

a

0 0

(4) t

a

0 0

AL/2020/01/E-I - 12 -

AL/2020/01/E-II(A) KOg;gjpg;GupikAilaJ / All Rights Reserved]

This question paper consists of 20 pages.

This paper comprises of two parts A and B. The time alloted for the two parts is three hours only.

Use of calculator is not allowed.

Part A – Structured Essay ( Pages 2 - 8 )

Answer all the questions on the question paper itself.

Write your answers in the space provided for each question.

Please note that the space provided is sufficent for the answers and that extensive answers are not expected.

Part B - Essay ( Pages 9 - 20 )

This part consists of six questions. Answer four questions only. Use the papers supplied for this purpose.

At the end of the time alloted for this paper, tie the two papers together so that Part A is on top and hand them over

to the Supervisor.

You are permitted to remove only Part B of the question paper from the Examination Hall.

For examiner’s use only

Final marks

In numbers

In words

Code numbers

Examiner 1

Examiner 2

Checked by

Supervised by

Part Question No. Marks

A

1

2

3

4

B

5

6

7

8

9(A)

9(B)

10(A)

10(B)

Total

Percentage

Index No. : .................................................. ........

[See page two

AL/2020/01/E-II(A) - 2 -

Do Not Write

Anything

Here

Answer all the questions in the paper itself.

g = 10 N kg-1

01.

(a)

i. Name the parts A, B, C, D, and F of the above shown vernier calliper.

A - ……………………………………………………………….

B - ……………………………………………………………….

C - ……………………………………………………………….

D - ……………………………………………………………….

F - ……………………………………………………………….

ii. Give the function of the parts E, G.

E………………………………………………………………………………………………………..………

G…………………………………………………..…………………………..……………………………….

iii. Answer the following questions by observing the magnified region given below.

1. What is the length of one vernier division? ………………………………..……………..

2. What is the least count of this instrument?…………………………..………..

iv. When the 7th division of vernier scale coincides with the main scale as shown in figure, denote the 0 line of the

verneir scale in the figure given below. (Indicate in the figure considering the instance mentioned above.)

v. The figures (a) , (b) indicate the position when measuring zero error and the thickness of an iron plate

respectively.

D

A

G

C

F

A

D

A

G

C

F

E B

[See page three

AL/2020/01/E-II(A) - 3 -

Do Not Write

Anything

Here

………………………………………………………………………………………………….

………………………………………………………………………………………………….

………………………………………………………………………………………………….

(b) All the parts of the shiny iron cylinder shown below can be measured using the above mentioned vernier calliper.

i. By which parts of the vernier caliper the following measurements can be taken?

d1- ……………………………………………………………..

h1- ……………………………………………………………..

d2- ……………………………………………………………..

h2- ……………………………………………………………..

ii. Give the expression for the volume V of the cylinder shown above in terms of the symbols given above . (The

right end of the cylinder is a hemisphere)

………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

………………………………………………………………………………………………………………………

………………………………………………………………………………………………………………………

02. You are asked to find the specific latent heat of fusion of ice using the method of mixtures in the laboratory.

(a) Draw a labeled diagram of the experimental setup you have used in that experiment.

(b) Although ice cube can be obtained in many forms, its preferred to use small pieces of melting ice. Give the

reason?

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

(c) What are the environmental factors that would affect the initial and final temperatures you expect?

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

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(d) When the dew point is approximately 2oC less than the environmental temperature on a particular day, it is

advised to use a thick plastic vessel with very less heat capacity to perform this experiment. Do you agree with

this statement? (Yes/No) Give the reason for this.

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

(e) The measurements and data given below are obtained from the experiment.

Mass of calorimeter with stirrer = 100g

Mass of calorimeter with water and stirrer = 250g

Temperature of calorimeter with water when starting the experiment = 36

Minimum temperature of calorimeter with water when finishing the experiment = 24

Mass of calorimeter with water and stirrer after adding ice = 275g

Specific heat capacity of water =

Specific heat capacity of the substance with which calorimeter and stirrer are made up of S =

i. Write an expression for the quantity of heat (Q) lost by calorimeter (with stirrer) with water in terms of the

symbols of quantities mentioned above.

……………………………………………………………………………………………………………

……………………………………………………………………………………………………………

……………………………………………………………………………………………………………

ii. Find the specific latent heat of fusion of ice.

……………………………………………………………………………………………………………

……………………………………………………………………………………………………………

……………………………………………………………………………………………………………

……………………………………………………………………………………………………………

(f) Denote ( ) in the appropriate columns to indicate whether the following errors done in the experiment cause the

value obtained for the specific latent heat of fusion from the experiment to be greater or lesser than the real

value.

Using ice cube at -20C

Using ice cubes without drying (wiping)

Dew depositing around the outer surface of calorimeter at the end

of experiment.

Lesser Greater

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03. Narrow uniform glass tube open at both ends, tuning fork of frequency (f) 512Hz and a tall vessel containing water are

given to you. An experimental setup has to be done in order to find the speed of sound in air (V) using method of

resonance.

(a) Draw a diagram to represent the experimental setup.

(b) How can you make sure that the air column resonates at its fundamental frequency?

………………………………………………………………………………………...………………………………

………………………………………………………………………………………...………………………………

(c) The lengths of tube above the water level for the first two resonating stages are measured as l0=15.8cm,

l1=48.0cm respectively.

i. Draw the wave patterns for the above two resonance states.

ii. Calculate the value obtained for the wave length of harmonics created by the tuning fork in this laboratory

environment?

……………………………………………………………………………………………………………

……………………………………………………………………………………………………………

……………………………………………………………………………………………………………

iii. Using a tube which can vary its length by moving a piston is more suitable than using above mentioned one

end closed tube with variable length. Justify this statement.

……………………………………………………………………………………………………………………

……………….………………………………………………...…………………………………………………

iv. Determine the value obtained for the speed of sound in the laboratory environment.

……………………………………………………………………………………………………………………

……………………………………………………………………………………………………………………

……………………………………………………………………………………………………………………

v. What is the another physical quantity that should be noted during the experiment in order to conclude your

result meaningfully.

……………………………………………………………………………………………………………………

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vi. The error of the calculated speed of sound (v) can be given using the expression below.

,

1

1

0

0 vl

l

l

l

f

fv

, 1 10 mmll

Hzf 24

Find the error ? ………………………………………………………………….………………………………………………

………………………………….………………………………………………………………………………

…………………………………….……………………………………………………………………………

………………………………………………….………………………………………………………………

vii. What is the range of value that can be obtained for the speed of air in laboratory?

………………………………………………….………………………………………………………………

04. The experimental setup for the determination of temperature co-efficient of resistance of a copper wire is given below.

Resistance of wire at 00C and θ0C are R0 and Rθ respectively. The resistance of resistance box in the circuit is R1.

Temperature (θ) of water has been changed by heating the water and balance length (l) for each state is obtained. After

that by using the graphical method temperature co-efficient of resistance α of the copper wire is obtained.

(a)

i. What are the other equipments required to perform the experiment perfectly?

………………………………………………………………………………………………………………………

……………………………………………………………………………………………..……………

ii. What is the experimental procedure that should be done in order to maintain the temperature of the wire coil at a

uniform value?

…………………………………………………………………………………………………………………

…………………………………………………………………………………………………………………

iii. Write an expression for in terms of , and ? …………………………………………………………………………………………………………………

iv. Write an expression for in terms of balance length and resistance of resistance box R1?

…………………………………………………………………………………………………………………

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v. Obtain a new expression while keeping as dependant variable in order to draw a straight line graph using

the above two expressions.

………………………………………………………………………………………………………………………

………………………………………………………………………………………………………………………

………………………………………………………………………………………………………………………

……….…………………………………………………..……………………………………………..……………

vi. Draw the expected approximate graph in the axis given below. How would you find the temperature co-efficient

of resistance of wire using the graph?

………………………………………………………………………………

………………………………………………………………………………

………………………………………………………………………………

………………………………………………….…………………………

…………………………………………………...………………………….

vii. A student proposed that the amount of current passed through the wire coil should be small in order to get an

accurate value for Explain the reason.

……………………………………………………….………………..……………………………………………...

……………………………………………….……………………………………………….………………………

………………………………………………………………………..…………………………….………………...

(b) Inorder to find the balance point in the above experiment, an electronic circuit comprising operational amplifier,

transistor and LED is used instead of center zero galvanometer. Here non inverting (+) and inverting (-) inputs

are connected to the points P, Q respectively.

i. If the potential at P is greater than that in Q, LED will light up or not?

……………………………………………………………………………………………………………

ii. If the potential at Q is greater than that in P, LED will light up or not?

……………………………………………………………………………………………………………

0 0

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iii. How can you examine whether the meter bridge is correctly working or not by using this electronic circuit?

……………………………………………………………..…………………………………………….

……………………………………………………………………..……………………………………..

iv. By using this circuit instead of center zero galvanometer, how can you get an accurate balance point?

…………………………………………………………………………..………………………………

……………………………………………………………………………………..……………………

v. If VBE = 0.7V and; RB = 430kΩ, calculate the base current through transistor when LED lights up?

(Saturation voltage of operational amplifier is 13.6V)

……………………………………………………………………………………………………………

……………………………………………………………………………………………………………

……………………………………………………………………………………………………………

……………………………………………………………………………………………………………

……………………………………………………………………………………………………………

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KOg;gjpg;GupikAilaJ /All Rights Reserved]

Part B – Essay

Answer four questions only

(𝑔 = 10𝑁𝑘𝑔−1)

05.

(a) Figure 1 denotes the simple structure of upper view

of an equipment which is used to practice balling in

cricket. It has two identical wheels of radius 16cm

which are coated by rubber. These wheels are rotated

by separate motors. At the moment of balling, by

using a proper mechanism, the cricket ball is slowly

released into the gap between those two wheels.

When the ball is released into this gap, as the both

wheels are rotating, they exert a force on the released ball and accelerate it. Therefore the ball is thrown out with

the required velocity. In cricket, when practicing in net, when there is no bowler, this equipment is used. The mass

and radius of the ball are 0.16kg and 3.6cm respectively. (Assume that the ball does not rotate and the ball does

not slip only at the instance when ball is thrown out of the wheel)

i. Copy the figure of wheels in the answer sheet and denote the direction of rotation of the wheels when ball is

thrown with the speed mentioned above in the direction shown.

ii. What is the angular speed with which each wheel has to rotate in order to throw the ball with the velocity of

144 kmh-1?

iii. Draw the outer view of the ball and denote the forces exerted on the ball by the two wheels.

iv. In between the wheels, the force is exerted on the ball for 0.016s by both wheels.Calculate the average force

given to the ball by a single wheel.

v. If the normal reaction between a single wheel and ball is 500N, calculate the co-efficient of kinetic friction

inbetween the surface of ball and rubber in the wheel.

(b) In another instance, a cricketer is involved in net practice using the above equipment. The equipment is directed

downward, inclined at a particular angle with the horizontal and the ball is thrown with the horizontal velocity of

40ms-1

and vertical velocity of 1ms-1. Assume that the ball releasing part of the equipment is at a height of 1.75m

Direction of ball motion

Ball

Ball

releasing

mechanism

Rubber

coated

wheels

Figure 1

[See page ten

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from the ground and length of the pitch for net practice is 21m. Equipment is fixed at one end of the pitch. At

opposite end, the cricketer faces the ball. (Neglect the air resistance)

i. What is the time taken by the ball to travel in air and collide with the ground for the first time after it has

thrown?

ii. At what distance from the opposite end of the place thrown, the ball collides with the ground?

iii. After the collision with the ground, horizontal velocity of ball is decreased by 20% and vertical velocity is

reversed and decreased by 20%. What is the speed with which the ball bounces up towards cricketer?

( 41 = 6.4)

iv. Just after ball bounces from the ground cricketer defends the ball by inclining the bat at an angle of 37° to

the vertical in order to make the horizontal component of velocity as zero. After 0.2s from the moment ball

touches the bat, the horizontal component of velocity of ball becomes zero. Calculate the average force

applied on the ball by the bat at this instance? (cos 37° = 0.8)

(c) Now the ball has to be thrown from the equipment with speed of 40 ms-1 and

rotating speed of 20 rads-1

, (Figure 2). For this, wheels of the equipment are made

to rotate at different speeds. Assume that at the instance the ball doesnot slip in

between two wheels when rotating ball throw takes place.

i. Calculate the angular speed with which each wheel has to be rotated in order to perform the above throw?

ii. If this ball is thrown towards the cricketer, for the cricketer to which side (right /left) the path of ball is

seemed to be deviating?

06.

(a)

i. Consider a situation where refraction takes place at critical angle between light penetratable substance of

refractive index n and air. In this situation draw the ray diagram and obtain a formula for the critical angle

using a proper law.

ii. Compare the critical angles for red and blue light rays between two particular mediums.

iii. Give the conditions for total internal reflection to take place.

(b) An optical fiber having square cross section of side

length d is bent to make a semi circle as shown in the

nearby two dimensional figure. Radius of inner semi

circle is r. At this instance, its width d remains constant

throughout the length. The light ray P incidents normal

to the square face as shown in the figure.

i. The light ray P in its continuing motion involves to two total internal reflections only and emerges from the

other square face perpendicularly. Draw a ray diagram for this.

ii. In order to have the path of ray P as mentioned in question (b) (i), what should be the distance between center

of semi circle and the incident point of P?

iii. Draw the continuous paths of rays which incident normal to the square face at a point just left and just right to

the point of incidence of P mentioned in question (b) (ii) above. (Assume that each of these rays involve to

total internal reflection only twice)

Figure 2

20rads-1

r

d

P

d

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iv. Give an expression for the least possible incident angle, an incident ray which incidents normal to the square

face could have when incident on the curved face for first time, in terms of r and d.

v. As mentioned in question (b) (iv) if the light ray which incidents on curved face, involves to critical total

internal reflection, give the refractive index of the optical fiber in terms of r, d. (Semicircular optical fiber is

kept in air)

(c) For military purposes, a special type of optical fiber is made in order to observe the disturbances that take place

above ground from a long distance. This optical fiber is fixed below the ground. It involves to compression during

disturbances above the ground and the refractive index of fiber in that particular compressed region will change.

Because of this, a part of light signal which is sent continuously from the observation center involves to partial

refraction at the region where the refractive index change took place and then returns to the observation center.

i. If the refractive index for red light in optical fiber medium is 1.5, what is the velocity of red light in the

optical fiber medium? ( Velocity of light in vacuum is 3x108 ms-1

)

ii. A red light ray which is sent along the axis of a straight, horizontal optical fiber incidents normal to a region

of optical fiber in whichthe refractive index is changed. If the time difference between the sent and reflected

ray ∆𝑡 = 50 𝜇𝑠, at what distance from observation center, the disturbance was made?

iii. If blue light ray is used instead of red light ray, the value of time difference ∆𝑡 calculated in question (c) (ii)

above will be greater or lesser than that for red ray?

07.

(a) One end of a capillary tube of uniform cross sectional area is immersed vertically into a vessel containing water.

Diameter of the capillary tube is d. Take density of water as 𝜌W, surface tension of water as T and gravitational

acceleration as g. Show that the expression for the height of water column ℎ0 can be given as gd

Th

w

40

in terms

of 𝜌W> T> d> g (Assume that the contact angle for water and the substance with which the capillary tube is made

up of is zero).

(b) Under the soil, below a particular level,

underground water is found. Each type of soil is

made up of soil particles. Gaps are found

inbetween these particles. These gaps join to

form capillary tube like structures in the soil.

Figure 1 shows that type of capillary tube

formed in a type of soil. In soil, water found in

the capillary tubes is called capillary water. The

height at which the capillary water found is

known as height of capillary water column.

Average surface tension of soil water is 7×10-2

Nm-1

.

i. By assuming that the contact angle for all type of soil and water is a constant of value α, write an expression

for the height h of capillary water column in terms of 𝜌w> T> d> g and α.

ii. Diameter of capillary of a particular type of soil is 0.004mm. Calculate the height of capillary water column

of that soil type. (cos𝛼 = 0.8)

Ground water level ;

Capillary water

h

Figure1 1

T T

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iii. Size of capillary (d) of different soil types depends on the size of one soil particle of soil. It can be given as

𝑑 = 𝑒𝐷0 . Here 𝑒 is a constant and 𝐷0 ; is the average size (diameter) of a soil particle. If 𝑒 = 0.2 what is the

average size of a soil particle mentioned in question (b) (ii)?

iv. If the contact angle for all type of soil and water are nearly equal, show that the height of capillary water

column for different soil types can be given by h=k

eD0 Here, k is a constant.. Determine the value of k.

v. The size of a particle of sandy soil and clay soil are 0.04mm and 0.008mm respectively.Which soil is most

suitable for agriculture? Explain why?

(c) The maximum stable inclination which can be made with the

horizontal ground by the dry sandy soil, which is poured to make a

pile when allowed to slip independently on the ground, is called as

resting angle.When sand particles are moistured to a small extent,

as surface tension of water in the capillary gaps tightly hold the sand

particles, the resting angle is increased in an amazing manner. Even

though, when the sand particles are moistured further, the capillary

gaps will be completely filled with water. Therefore there will be a

loss in the frictional contact between sand particles which will

cause sudden decrease in resting angle. So sand particles will show the properties of a fluid. But clay soil particles

contain minerals which are soluble in water. These minerals in clay soil dissolve in water and allow the clay

particles to slip and at the same time, in dry state, it helps to hold the clay soil particles tightly. Clay soil allows the

water to slip more than sandy soil. When excess amount of water is added to clay soil, there is a considerable

increase in the volume of clay soil, and therefore clay soil shows fluid nature. Because of this stability of clay soil

is less than that of sandy soil. Because of these effects, when we walk in wet clay soil our feet get sunk more than

when we walk in slightly wet sand. But in sandy soil having excess amount of water, feet will sunk easily.

(i) What is the reason for the increase in resting angle of sand when the moisture of sand in increased to a small

extent?

(ii) If the height of sand pile is 30cm and the diameter of pile is 60 3 cm, calculate the magnitude of resting angle

of dry sandy soil.

(iii) In the morning, by using wet sand soil, a child is forming a wet sandy soil pile in the beach. What will happen

to the height of sandy soil pile and its base area due to the drying of soil? (The resting angle of wet sand is

twice than that of dry sand)

(iv) In the afternoon due to the heat from sun, the sandy soil pile is completely dried. Assume that there is no

change in the amount of soil found in the sand pile. If the resting angle of sandy pile after drying is equal to

the resting angle of dry sand that you have calculated above, and if the height of wet sand pile made by that

child is 9cm, calculate the height of that soil pile after drying. (Volume of cone= 1

3πr2h)

(v) The structures constructed using proper moisture clay soil remain undestructive even during dry condition.

Give reason for this.

(vi) Two regions A, B are selected to construct solid waste management station. The soil at A is more clayey and

the particles of soil at B has gravels which have particles larger in size than clay. In which of the above

mentioned region it is suitable to construct a purifying station inorder to reduce water pollution? Give reason.

θ

Figure 2

Resting angle

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08.

(a) Write the equation of Newton’s inverse square law which explains gravitational attraction between two masses and

identify each quantity in that equation.

(b) Write a formula for the gravitational field strength g at a point which is at at a distance of x ( x > R) from the center

of an object of mass M and radius R. (Universal gravitational constant G)

(c) In order to analyze the surface of moon, a satellite is sent from earth. It travel a long distance and reaches near the

moon.Then, it revolves around the moon in a certain circular orbit with a uniform speed Vor. This orbit is at about

h=170 km from the surface of moon. Mass of that particular satellite is 1×103 kg. With that, radius of moon

RM = 1.7 × 103 km. The gravitational field strength on moon surface gM

= 1.7 Nkg-1.

i. Write the formula for the orbiting speed Vor of satellite in terms of gM

, RM, h. Hence, find the value of Vor.

95.087.1

7.1

ii. What is the minimum speed Vesc required for the satellite

which is at h = 170 km from the moon surface in order to

escape from the gravitational field?

iii. When the satellite reaches point P, if its speed is equal to Vor

it will orbit along path B and if its speed is equal to Vesc it

will orbit is along path D. Give the ranges of speed for the

orbits A, C, E?

(d) Certain satellite which is rotating in a circular orbit nearby the

surface of moon moves in an elliptical path as shown in Figure.

When it nears the point Q, its orbit is converted into a circular

orbit nearby the surface of moon and the satellite is allowed to

move in that orbit. If the speed of satellite at the initial point P is

v, (use the data in (c) for calculations)

i. Find the speed of satellite at the end of elliptical path in terms

of v (At point Q, neglect the height of satellite from moon

surface)

ii. If the mechanical energy is conserved at the above mentioned points P, Q, give reason for that and by using

this principle, show that the speed of satellite v at initial point of oval path is 1.58 kms-1

. Hence, find the speed

of satellite at point Q in kms-1

.

iii. Calculate the speed required by the satellite in order to move near the surface of moon in circular orbit.

iv. Calculate the impulse required to change the path of satellite as elliptical at point P?

P A B

C

D

E

A

Moon

Figure

P Q

Initial circular path

Final circular path

Oval path

Moon;

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v. Calculate the impulse required to change the path of satellite as circular at point Q?

vi. Compare the kinetic energy per unit mass, potential energy per unit mass and total mechanical energy per unit

mass of satellite in the elliptical path at points P, Q. (Consider the elliptical path motion)

vii. Is it possible to land the satellite on the surface of moon with the speed calculated at Q above at the end of

elliptical path? Give reason for your answer.

09. Answer either Part(A) or Part(B) only.

(A) Answer the following questions according to the paragraph given below.

Wireless charging or induction charging is the process of charging electric devices without wire. Nowadys

this method is popular for charging small devices. By using this method smart phones, smart watch and

tablet can be charged. In addition to this, in vehicles and medical equipments induction charging is used. Qi

method is used to denote the technical standard of induction charging. Under this method many popular

technology companies like Apple, Samsung and Asus work together to improve wireless charging.

Wireless charging is based on electro magnetic induction. Because of this, it is

called as, induction charging. In this method by using a charging pad, electric

devices are charged. The charging pad has a primary coil. It is also known as

exchanging coil. A varying current is passed through the exchanging coil. That

current creates a varying magnetic field around that coil. According to

Faraday’s induction law, electro motive force is induced in the secondary coil

of the electric device.The coil in the electric device is called as receiving coil.

Most of the electric devices can work only in direct current. To charge their battery, direct current is

important. Therefore the alternating current obtained in receiving coil is converted into direct current and

then used to charge battery of an electric device. During charging, both charging pad and electric device

have to be kept closer. Other than charging electric devices, another main use of wireless charging

technology is to charge electric vehicles. For this, charging pads are constructed nearby the roads and in

vehicle parking stations. Under these vehicles, receiving coil is fixed and connected with the battery. When

vehicles are parked at parking stations, batteries of vehicles are charged. Then during travelling, by using the

energy stored in batteries, motors are operated. When energy stored in batteries are not enough to travel, the

vehicles can be parked in electric vehicle charging stations which are in nearby the roads and can be

charged using charging pads. Then the journey can be continued. As charging pads consume relatively high

current, it is not preferable to use common supplying wires in the construction of vehicle charging stations.

Because of this, to supply current for vehicle charging stations, it is vital to use thick wires and individual

transformer systems.

(a) Give two important uses of wireless charging

technology.

(b) What are the two major components used in induction

charging method?

(c) Briefly describe how electric devices are charged by

using wireless charging technology.

(d) It is not good to use metal parts near the receiving coil

present in the bottom part of electric vehicles. Give the reason for this.

Exchanging coil

Receiving coil

Charge controller

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(e) Exchanging coil of a charging pad which is used to charge a smart phone contains 60 turns. It is

connected to the normal house electric circuit (240V alternating current supply). Give the maximum

magnitude of electromotive force induced in a receiving coil having 2 turns?

(f) A lithium battery used for the smart phone mentioned in (e) above is of 3.7 V DC electromotive force and

has an internal resistance of 0.15 Ω. The induced emf in the receiving coil which is mentioned in above

question is converted into constant voltage of 4V with the help of an organizing system and supplied in

between ends P, Q. The above figure shows a circuit for this process. In the circuit R is a permanent

resistance which is connected in series with the battery. The maximum current that can flow during charging

process without affecting the battery of a particular smart phone is 200mA.

i. Identify the polarity terminals P, Q for correct charging. (positive/negative)

ii. Calculate the minimum value of resistance R should have in order to charge without affecting the

smart phone’s battery?

iii. While using R with value calculated above in question (ii), calculate the power discipated in the

internal resistance of battery and in R during the charging process.

iv. The efficiency of this charging is given by the formula 𝑃𝑜𝑤𝑒𝑟 𝑢𝑠𝑒𝑑 𝑡𝑜 𝑐ℎ𝑎𝑟𝑔𝑒 𝑏𝑎𝑡𝑡𝑒𝑟𝑦

𝑇𝑜𝑡𝑎𝑙 𝑝𝑜𝑤𝑒𝑟 𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑑 𝑖𝑛𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑒𝑛𝑑𝑠 𝑃,𝑄 ×100%.

Calculate the efficiency of the above charging process.

v. Another company produced a smart phone with lithium battery similar to the above battery which

requires less time for charging with the same emf and internal resistance as above mentioned battery.

For this, whether the minimum value of the resistance that should be connected in series with the

battery should be greater or lesser than the value calculated in (ii) above? Give reason. (In this question

also assume that the voltage supplied in between ends P, Q is 4V)

vi. Is the life time of the battery mentioned in (v) above is greater than that of the battery mentioned

earlier? Give reason for your answer.

(g) An electric vehicle has to travel to a city which is at 200km distance. Its battery’s electric storage is 80Ah.

Now, only 12.5 percent of electric storage is remaining in the battery. To drive the vehicle at speed of

30 km h-1, a constant current of 2A is taken from the battery. Assume that the current is taken as directly

propotional to the speed of the vehicle.

i. Show that the vehicle cannot reach the city without electric re-fill.

ii. Vehicle had stopped as the electric storage of battery is finished. If he decides to travel the remaining

distance within 1 hour after the electric re-fill, for how long the vehicle has to be charged in an instant

vehicle charging station where charging takes place at a rate of 13.33A.

3.7 V Receiving coil

;

P

Q

Organising system

;

r = 0.15Ώ

R

[See page sixteen

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(B)

(a) The current gain of the transistor shown in figure is

100, and the voltage required to forward bias the

base-emitter junction is 0.7V. The voltage difference

between collector and emitter in the saturation stage

of transistor is 0.1V.

i. Calculate IC when the transistor is in saturation stage.

ii. What is the minimum value for IB in order to operate the transistor in saturation stage?

iii. What is the minimum value for V1 in order to operate the transistor in saturation stage?

iv. This circuit resembles the operation of which logic gate if only 0V and 5V are supplied for V1?

(b) Most of the human inventions are made according to the observation of nature. Artificial Neural Networks (ANN)

is one of the most popular technology nowadays and considered to be the first step towards Artificial intelligence.

It is developed based on the neurons in human brain. Commonly they are implemented by computer programs but

sometimes they are implemented by electronic circuits too.

The figure shown below is such an electronic circuit which is the basic unit of a neural network.

In the above picture, the electronic circuit inside the box is unknown. The relationship between V1> VA and VB

are given below. Here VA and VB are the voltage at ends A, B respectively.

V1 = 5 θ0 + θ1VA+ θ2VB

Here the values of θ0, θ1, θ2 can be changed according to the requirement. For A, B inputs, only 0V or 5V is

given always. Therefore when changing θ0, θ1, θ2 different logic gates are obtained between A, B at Vout(V) is

a special feature.

i. At an instance, θ0 = 2, θ1 = -1, θ2 = -1. For this instance, copy the following table in your answer sheet and

fill in the table.

VA VB V1 V0ut

0V 0V

0V 5V

5V 0V

5V 5V

ii. Give the truth table for A, B, F based on the table you filled in question (b) i above. Give the logical

relationship between A, B, F for this instance and also mention which logic gate is resembled by that circuit.

The following diagram method is used to denote neural network easily. In this method, the circuit in Figure-1

can be drawn as follows.

+5V 1 kΩ

82 kΩ

IB

V1

Vout//F

VA

VB B

A

Figure-1

+5V

1 kΩ

82 kΩ

IB

V1

Vout

Ic

[See page seventeen

Al/2020/01/E-II(B) - 17 -

Water

Layer of ice

iii. Give the truth table for A, B and F for the situation shown in figure 3.

iv. Which logic gate is represented in the circuit given above in question (B) (iii)?

v. If the figure 4 shown below denotes OR gate ( F = A + B ), select the most suitable value for m from the

values given here? -1, -0.5, 0, 1, 2

vi. Give the truth table for A, B, C, D, E, F to

represent the neural network shown in figure 5.

From this give the logical relationship between A,

B and F and write the logic gate which resembles

this logical relationship? (C, D which are denoted

here are similar to F in figure 2)

10. Answer either Part(A) or Part(B) only.

(A) The figure shows a pond which is freezing during winter in a country near the polar region.This pond can be

considered to be with uniform circular area of cross section of radius 50m. Initially it has liquid water to a height

of 10m and on its surface, a layer of ice about 1.25m thickness is found. Assume that the temperature at the

contact point of water and ice is always taken as 0 and the temperature of upper surface of ice is −5.

(Thermal conductivity of ice is 2.0 Wm-1

K-1 and specific latent heat of fusion of water is 3 × 10

5 Jkg

-1) (Take

𝜋 =3)

Figure 2

+5

A

B

F θ 1

θ 2

θ 0

Figure 3

+5

A

B

F 2

2

-1

Figure 4

+5

A

B

F -1

m

1

Figure 5

+5

A

B

F

D

C

-1

-1

-1

+5

1

-1

2

2

m

2

[See page eighteen

Al/2020/01/E-II(B) - 18 -

(a) Due to the heat flow through the ice layer, the thickness of ice layer increases gradually with time.In this

state assume that the transfer of heat from the water at bottom of pond to the lower surface of ice layer can

be neglected.

i. Determine the rate of heat flow across the layer of ice in this condition. In which direction that heat

flow would take place?

ii. By using the answer obtained in (i) above calculate the rate at which the thickness of ice would

increase. From this, show that the increase in the thickness of ice for a short period can be neglected.

(Density of ice is 800 kg m-3)

(b) Magma intrudes the nearby floor part of the pond due to small explosion caused in the earth plates which

are found in bottom of the floor of pond. 2400W of heat is obtained at a constant rate from this magma.

This total heat gets transferred through water in the vertically upward direction. In this situation any

convectional currents were not observed in water. The temperature of outer surface of ice layer is found to

be at -5°C. (Thermal conductivity of water is 0.8 Wm-1

K-1

)

i. By considering the heat flow through water, calculate the temperature of water at the bottom of pond.

ii. Using the answer obtained in part (b) (i) above, give the reasons why convectional currents do not

take place in pond at these conditions.

iii. In this time, what would happen to the rate of increase in thickness of ice layer (will it increase or

decrease) than the rate obtained in (a) (ii) above?

iv. Loss of heat from the outer surface of ice to the environment takes place according to the Newton’s

cooling law. Calculate the temperature of air above the ice layer. ε = 1.6 Wm-2K-1 for the surface of

ice. (Rate of heat loss according to Newton’s cooling law can be given by the equation

).( RAdt

dH Here, ε is a constant which depends on the type of surface, and A is the effective

area through which heat loss takes place. θ, θR are temperature of surface and temperature of

environment respectively.)

(c) In part (b), at a particular instance, due to changes in the external environment, the temperature of air above

the ice layer changes and the temperature of surface of ice layer becomes stable at less than 0°C. Therefore

in the above condition, although heat flow takes place through the ice layer of pond, additional increase in

the thickness of ice is not observed. Calculate the temperature of outer surface of ice layer at this condition.

(d) In the condition stated in (b), consider a fish living in the pond water and adapted to cold climate. The fat

layer below the skin of fish maintains the internal temperature of body at a value considerably greater than

the temperature of water. Therefore, the fish can survive even under extreme conditions. As fish is in the

cold water, there is a continuous heat loss at a constant rate from the body of fish to the environment across

its fat layer. To compensate this, fish produces heat through metabolism.

At steady state, if the internal temperature of the particular fish decreases than 15, the fish would die. The

effective surface area through which heat loss takes place in fish is 60cm2. The thickness of fat layer in fish

is 1cm and the thermal conductivity of fat layer is 0.2 Wm-1

K-1

. Assume that the thickness of skin of fish

can be neglected.

[See page nineteen

Al/2020/01/E-II(B) - 19 -

i. If the temperature of outer surface of skin of fish is 3°C, what is the minimum rate of heat production

that should take place by metabolism of fish in order to survive in that particular environment?

ii. A researcher observed that the particular fish spends most of the time in the bottom part of the pond.

Give the possible reason for this.

(B) (a)

(i) Write the formula for the energy radiated in unit time from a black body of surface area

A at temperature T K.( Stefan’s constant 𝜍 )

(ii) As shown in (figure 1), a black body is kept in an environment of temperature T0 K.

Due to this, energy is radiated from environment into that particular black body.

Environment can emit all wavelengths. Therefore it’s a black body. Write the formula

for the energy radiated from environment to the black body in unit time.

(iii) From this show that the equation for the net emission power of the radiation from the surface of the particular black

body can be given as P = 𝜍A(T4 - T0

4).

(iv) In the situation where the surface temperature of black body is equal to the environmental temperature, what is the

net emission rate of radiation from the surface of the black body?

(b)Temperature gun is an equipment which is used to measure the temperature without any

contact (Figure 2), works according to the black body principle. It has a special sensor

bulb. The surface area of sensor bulb is A. Its surface temperature is T K. Another sensor in

temperature gun is used to measure the average temperature of the environment directly.

(Take it as T0 K). In the case where temperature has to be measured without contact with the

surface, the temperature gun is kept near the surface where temperature has to be measured.

In this instance, the radiation radiated from the same area (A) as that of area of sensor bulb,

incidents on the sensor bulb with the same intensity. Photons of incident radiation make the

electrons in the substance in bulb to excite to higher energy levels.

When these electrons come back to lower energy levels, they produce an electric signal. From this signal, the gun

calculates the emitted or absorbed net power (P) from the radiation from sensor bulb. Gun takes P as positive when

emission takes place as net and takes P as negative when absorption takes place as net. Neglect the change in the

temperature of the particular sensor bulb in this process. According to the programs in temperature gun, the surface

temperature of the particular object can be observed in screen. Assume that the surface temperature of an object for

which the temperature has to be measured is TX K. (𝜍 =5.6 ×10-8

Wm-2

K-4)

(i) Most of the surfaces for which the temperature has to be measured are not black bodies. The emitting ability of

their surface at a particular temperature will vary according to the type of their surface. Take it as ϵ. Give the

formula for the energy emitted from the body of area A of which the temperature is measured in terms of ϵ> TX> 𝜍>

A.

(ii) Show that the equation for net emission power from the sensor bulb is given by, P = 𝜍A(T4-T0

4-ϵTX

4).

(iii) Hence, write an equation for determining the temperature TX of a particular surface. (Assume that in all cases, the

power emitted from the environment to the sensor bulb remains constant)

This equation is included in the electronic circuits of the temperature gun. Using this, the temperature gun performs

calculation and gives the temperature of the surface for which the temperature has to be measured in the display.

(Figure 2)

T0 K

T K

cU 1

[See page twenty

Al/2020/01/E-II(B) - 20 -

(iv) Temperature gun is used at an instance in order to measure the temperature of the person who enters into a shop. It

is given that the environmental temperature and the temperature of sensor bulb are 27°C and 30°C respectively. The

net emission power measured by sensor bulb is (-0.050W). If people with body temperature greater than 38 are

not allowed to enter the shop due to the corona pandemic, determine whether that particular person will be allowed

to enter the shop or not. Here, surface area of sensor bulb A=1cm2 (Take ϵ = 0.9 for that person)

Hint: 65.3129.0

1093.830030325.0

944

(v) If the environmental temperature in question (iv) decreases, what will happen to the measured surface temperature

( will it be equal to/ greater than/ lesser than the value obtained in (iv)). Give reason.

(vi) Another person with different type of skin surface comes to the shop. While observing him the value of ϵ of the

equipment was not changed. When the reading is taken, his surface temperature is measured to be 34.86. The

temperature of sensor bulb and environment are assumed to be remained as same mentioned in (b) (iv) above.

(There is a feature to change the value of ϵ according to the type of surface for which measurement is taken)

(i) Calculate the power calculated by the sensor bulb?

Hint : 844 1029.3300303 > 94 1058.986.312

(ii) From the equation obtained in question (b) (ii), assuming that ϵTX4 is a constant in both instances when the

equipment measured correctly and wrongly, calculate the real temperature of the person. Emissivity of the surface

of person = 0.88, Hint : 86.312

40.309

88.0

9.025.0

(vii) In some cases, there are regions with different temperature on the same surface where temperature has to be

measured. In that case, will the temperature measured by the gun be the average temperature of that particular

surface? Give reason.

(viii) Comment on the reasons why this temperature gun is not used to measure accurate temperatures in medical field.