physics manual xi

7/23/2019 Physics Manual XI

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1. USE OF VERNIER CALLIPERSAim : To determine volume of solid sphere and measure inner diameter, depth of hollow cylinder.

Apparatus : Vernier calipers, solid sphere, hollow cylinder.

Diagram :

Formula : Volume of solid sphere (V) =4

3

3R

Procedure :

1. Note the smallest division on the main scale of vernier callipers and the total number of divisions on

the vernier scale, hence find the least count vernier callipers using the formula

Least count =( )

( )

smallest division on the main scale of vernier callipers s

Total number of divisions on vernier scale N

2. To find the zero error of vernier callipers bring the two jaws of vernier callipers in contact. Observe

and conclude according to the following given conditions.


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a)

If zero division of main scale coincides with

zero division of vernier scale.

There is no

zero error.

b)

If zero division of vernier scale is on right(ahead) of zero division of main scale and if

mth

division of vernier scale coincides withsome division on main scale.

Zero error

= +m L.C.

c)

If zero division of vernier scale is on left

(behind) of zero division of main scale and if

mth

division of vernier scale coincides with

some division on main scale.

Zero error =

- (N - m)

L. C.

3. To determine the volume of sphere

Hold the given solid sphere between the lower jaws of vernier callipers as shown. Note the position

of the zero mark of vernier scale on the main scale.Let this main scale reading be A. Note the

vernier division (n) that coincides with some division on main scale. Then calculate the total reading

(T) with formula T = A + (n L.C.) Take atleast three independent reading for different positions of

the sphere. Apply correction according to zero error (T

Z) and find the mean value of diameter(D). Hence radius of sphere (R) =

2

D

4. To Find the inner diameter of hollow cylinder use upper jaws as shown in the figure. For depth use

depth gauze of the vernier callipers.

5. Calculate the volume of sphere.

Observation : Least count of vernier callipers.

Obs

No.

Description Symbol Value Unit

1.

2.

3.

4.

Smallest division on main scale

Total number of divisions on vernier scale

Least count

Zero error (with proper sign)

S

N

L. C. = S

N

Z. E. (Z)

cm

cm

cm.


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Observation table

Object Obs.No.

Dimensions MainScale

ReadingA cm

VernierScale

DivisionCoinciding

n

VernierScale

Readingn LC = B

cm

TotalReading

T=A+Bcm

CorrectedReading

T Z cm

MeanReading

cm

Sphere

1

2

3

Diameter

Cylinder

1

2

3

Inner

diameter

Cylinder

1

2

3

Depth

Calculations :

Radius of the sphere R = ----- cm

Volume of sphere

V = 34

3R

V = 34

(3.142) ( )3

V = ---------- cm 3

Result :

i) Volume of the sphere = ________ cm 3

ii) Inner diameter of hollow cylinder = ________ cm

iii) Depth of hollow cylinder = _______ cm.

Precautions :

i) While taking reading, do not press the jaws too hard.

ii) The different reading for diameter of an object should be taken a t different positions.

iii) While recording reading, eye should exactly be perpendicular to vernier scale.

Symbol Value Log

-

R

4

3.142

3R

3

+

+ N

D

V

Al( ) N D


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Page 4

2. USE OF MICROMETER SCREW GAUGE

Aim : To measure cross sectional area of uniform wire and the thickness of plate.

Apparatus : Micrometer screw gauge, plate, a metal wire of uniform diameter.

Diagram :

Formula : Least count of micrometer screw gauge.

Least count =Pitch of the screw

Total number of divisions

on circular scale

=P

N

Procedure :

I) To find the least count of screw gauge :

Note the value of the smallest division on main scale of screw gauge and total no. of divisions on the

circular scale of micrometer screw gauze. Note the distance travelled by the screw on main scale for

10 complete rotations of circular scale. Hence find the pitch of the screw and least count of the screw

gauze.

II) To find the zero error :

Bring the two jaws of gauge in contact with each other. Observe and conclude according to the

following given conditions.

a)If zero of circular scale coincides

with reference line.

There is no zero error. (Z) = 0


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III) To determine the diameter of wire, hold the wire between the jaws of micrometer and note down the

main scale reading (A) and the circular scale division that coincides with reference line, hence

calculate the total reading (T) with the following formula T = A + B.Take three independent

readings for different positions of the wire.

Find the corrected reading according to the zero error (T Z) and find the mean value of diameter

of wire. Do the similar procedure for finding thickness of the plate.

Observations :

Obs.

No.

Description Symbol Value Unit

1.

2.

3.

4.

5.

6.

7.

8.

Smallest division on main scale

Number of rotations to screw

Distance advanced by screw in 10 rotations

Pitch of the screw (P = X/10)

Total number of divisions on the circular scale

Least count of screw gauge

Zero error (positive / negative) division

Zero error ( m L.C.)

S

X

P

N

L.C.=P

N

m

Z

10

cm

cm

cm

cm

div

cm

b)

If zero of circular scale is below

reference line.

If mth division of circular scale

coincides with reference line.

There is Positive error (Z)

= + (m L.C.)

c)

If zero of circular scale is above

the reference line.

-If mth division of circular scale

coincides with reference line andN is total number of division on

circular scale.

There is negative error (Z)

= -[(N m) L.C.]


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Observation Table :

For diameter of the wire and thickness of the plate.

Object Obs.

No.

Dimensions Main

Scale

reading

A cm

Circular

Scale readingC.S.D. L.C.

= B

Total

reading

T=A+B

Corrected

reading

T Z cm

Mean

cm

Wire

1.

2.

3.

Diameter D = -----cm

r =2

D -----

Plate

1.

2.

3.

Thickness

t = -------

Calculations :

Area of cross-section

of wire a = 2r

a = 3.142 ( -----) 2

a = ---- cm 2

Results : i) Cross sectional area of wire (a) = _______ cm2

ii) Thickness of plate (t) = _______ cm

Precautions :

1) While rotating the micrometer screw, do not apply an excessive pressure on the object.

2) Use the ratchet to avoid the excessive pressure.

3) The screw sleeve should not be rotated instead of its head.

4) The screw should more freely without friction.

5) The zero correction, with proper sign should be noted very carefully and added algebraically.

Symbol Value Log

r

3.142

2r = ---

---

+

+

a Antilog =


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Page 7

3. SPHEROMETERAim : To determine the radius of curvature of a given spherical surface by a spherometer.

Apparatus : Spherometer, plane glass plate, watch glass, scale.

Diagram :

Formula : Radius of curvature of a spherical surface,

R =

2

6 2

d h

h where d = mean distance between two legs of a spherometer

h = sagitta of the spherical surface.

Procedure :

i) Press the spherometer on a plane paper so that it produces impressions of the tips of its three legs on

the paper.Measure the distance d1, d2 , d3 between the three marks of the legs. Hence find the mean

distance d between the legs.

ii) Find the least count of the spherometer and Place the spherometer on the plane glass plate.

Rotate the screw till the tip of the screw just touches the glass surface. This can be ensured by

observing that the tip of the screw coincides with its image in the glass plate.

iii) Note down the main scale reading (A), by observing position of the edge of the circular scale on the

main scale. Note circular scale reading (B) by observing the circular scale division coinciding with

the edge of the main scale hence find the total reading (A + B). In this way, take three observations

and calculate its mean.

iv) Raise the screw through some distance. Place the spherometer on a concave surface / convex surface

of the watch glass. Rotate the screw so that its tip and all legs of the spherometer touch the surface.

Again note down the main scale reading and circular scale reading hence find the total reading.

v) Take three observations and calculate its mean.

Observations :

i) Distance between the legs, d1= _______ cm, d2 = _______ cm, d3 = _______ cm.

mean distance, d =1 2 3

3

d d d = ________ cm

ii) Smallest division on main scale = ________ cm.

iii) Distance through which the screw advances on the main scale in 10 rotations of the circular scale,

l = _____ cm.

iv) Pitch of the screw, P =10

l= _____ cm.


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v) Total number of divisions on the circular scale, N = _____

vi) Least count (L. C.) of the spherometer =P

N ______ cm.

Surface Obs.

No.

M. S. R.

A cm.

Coinciding

Circular scaleDivision

C

C. S. R.

B=C L.C.

Total reading

T=A+B = cm

Mean

reading

Plane glasssurface

1

2

3

X = ____ cm.

Concavesurface

1

2

3

Y = ____cm.

Convex

Surface

1

2

3

Z = cm.

Calculations :

Sagitta for the concave surface, h1= Y X = ________ cm

Sagitta for the convex surface, h 2 = Z X = ________ cm.

21

1

16 2

hdRh

2

22

26 2

hdRh

Calculation Table :

For 1R For 2R

log 2d a log 2d a

log 6h1= b = log 6h 2 = b =

a b = c a b = c

R1 = Antilog1

2

hc R2 = Antilog

2

2

hc

Result : Radius of curvature i) for concave surface = ____________ cm.

ii) for convex surface = ____________ cm.

Precautions :

i) Measure distance d accurately.

ii) Consider lowest mark on the main scale as zero mark.

iii) Rotate the screw gradually so that tip of the screw just touches the centre of the curved surface.


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4. STATIC FRICTION

Aim : To study the relationship between force of limiting friction and normal reaction and to find

coefficient of static friction between a block and a horizontal surface.

Apparatus : Rectangular wooden block with hook, string , rough balance, weight box, pan, horizontal

plane surface with pully.

Diagram :

Formula : Coefficient of static friction =s

P

W

where P is the effort and W is the Load.

Procedure :

Note the weight of wooden block and pan separately using rough balance.

Keep the wooden block on horizontal surface. Tie one end of string to the hook of the block, pass the

string over pully and connect its free end to the pan. The string should be parallel to the horizontal plane.

Add the weight gradually to the pan till the blockjust beginsto move on horizontal plane. Note theweight (P 1) in the pan. Find the effort (P = P 0 + P1) required to move the wooden block (load)

Place a weight of 50 g on the block and repeat the above procedure. Take five readings by

increasing the weight on block by steps of 50 g. Calculate the coefficient of static friction using the formula.

Plot the graph of effort (P) along Y-axis and load (W) along X-axis. Calculate the slope which gives

the value of coefficient of static friction .s

Observations :

1) Mass of the empty block, W 0 = ________ g wt

2) Mass of the empty pan, P 0 = ________ g wt

3) Acceleration due to gravity, g = 980 cm/s 2


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Mean s= ___________

Calculations :

Observation 1 2 3 4 5

Log (P) = a

Log (W) = b

(a b) = c

Antilog of c = s

Graph

Result :

1) Coefficient of static friction by calculation, s = _________

2) Coefficient of static friction by graph, s = _________

Precautions :

1) The string (between block and pully) should be parallel to horizontal plane.

2) The pan should hang freely without touching the table.

3) Starting position of the block must be same for all readings.

4) Clean the horizontal surface and wooden block with blotting paper (or cloth paper)

Obs.

No.

Mass on

the block

W 1g

Total load

W = W 1+ W 0

g wt

Mass in the

Pan P 1g wt

Effort

P = P 1+ P 0

g wt

Coeff. of

Static

Friction =

s = P/W.

1

2

3

4

5


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Page 11

5. OHMS LAWAim : To determine resistance per cm of a given wire by plotting a graph of potential difference versus

current.

Apparatus : Uniform metal wire of unknown resistance, voltmeter, ammeter, battery / power supply,

rheostat, meter scale, one way key, connecting wires etc.

Circuit Diagram :

Formulae : 1) R =V

I

2) Resistance per cm of a wire = =R

L

Procedure :

Arrange the apparatus as shown in the circuit diagram and make the connections.Determine the least

count of voltmeter and ammeter. Close the key (K) and adjust the rheostat, such that a minimum current

passes through the resistance wire. Note down potential difference (V) and corresponding current (I).

Repeat the above step for different values (V) and corresponding current (I). Calculate the resistance in each

case. Plot the graph of V versus I. Determine the slope of a graph, which is the resistance (R) of wire.

Observations :

1) Length of a given wire = L = _______ cm.

2) Least count of ammeter = ________ A = _________ mA

3) Least count of voltmeter = ________ V

To determine resistance of wire (R).

Sr. No. I

(mA)

I

(A)

V

(volt)R =

V

I( )

1

2

3

4

5


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Calculations :

Obs. No. 1 2 3 4 5

log V = a

log I = b

a b = c

R = antilog c

1) Resistance per cm of wire =R

L

------------- / cm

Graph :

Slope =AB

BC

Slope =V

RI

---------------

2) Resistance per cm of wire = =slope

L = - - - - - / cm

Result :

1) Unknown resistance of wire by calculation = ____________

2) Unknown resistance of wire by graph = ____________

3) Resistance per cm of wire by calculation = ____________ / cm

4) Resistance per cm of wire by graph = ______________ / cm

Precautions :

1) The connections should be neat and tight.

2) The key should be inserted only, while taking the observations to avoid the heating of resistance.

3) If the deflection of the pointer in the voltmeter or ammeter is between any two divisions, then adjust

the rheostat so that the pointer coincides exactly with one of the division and then take the readings.


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6. R. I. OF LIQUID

Aim : To determine the R. I. of a liquid (water) by using concave mirror.

Apparatus : Concave mirror, plane mirror, retort stand, index pin, string, half meter scale, liquid

(water).

Ray diagrams :

Formula :

1) R. I. of liquid using concave mirror = = 1

2

R

R

where R1is the distance between pole of mirror and pin without liquid. R2 is the distance between

surface of water and pin.

Procedure : R. I. of Liquid using concave mirror :

1) Keep the concave mirror on the horizontal surface, with its reflecting surface upwards.2) Fix index pin horizontally in a clamp with retort stand and keep its tip on vertical line through pole

of mirror.

3) Coincide tips of the index pin and its image. (a) Move the index pin up and down and remove the

parallax between tips of the pin and its image seen in the concave mirror.

4) Note the distance (R1) between tip of index pin and pole of concave mirror using half meter scale.

5) Take small quantity of water in concave mirror, lower the index pin and remove the parallax

between its tip and tip of the image as seen through water. Note the distance (R2 ) between tip of

index pin and surface of the water using half meter scale.

6) Using formula determine R. I. of liquid.

7) Take three independent sets of R1and R2 .

Observation table :

Obs.

No.

Distance between

Pin and mirrorWithout liquid

R1(cm)

Distance between

Pin & surfaceof liquid

R2 (cm)

R. I. of

Liquid

1

2

R

R

Mean

R. I. ofliquid

1

2


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3

Calculations :

1) 1

2

R

R

Result :

(1) R. I. of given liquid using concave mirror

= _ _ _ _ _ _Precautions :

1) The tip of the pin should lie on the principal axis of concave mirror.

2) While removing the parallax, the eye should be kept at a minimum distance of 30 cm from the index

pin.

3) Parallax should be removed between index pin and image of index pin.

4) Take sufficient quantity of liquid in the concave mirror.

5) The liquid should be clean and transparent.

6) The index pin should be clamped horizontally.

Symbol Value Log

1

2

R

R

_ _ _ _

_ _ _ _

-

Antilog=


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12) Similarly make a scale of least count 5 mm or 0.5 cm


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physics manual xi

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