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This question paper consists of 25 printed pages

MERIDIAN JUNIOR COLLEGEPreliminary ExaminationHigher 2

_______________________________________________________________________

H2 Physics 9646/3

Paper 3 20 September 2011

2 hours

_______________________________________________________________________

Class Reg Number

Candidate Name _____________________________

READ THESE INSTRUCTIONS FIRST

This booklet contains Sections A and B of the Preliminary Examination Paper 3.

Do not open this booklet until you are told to do so.

Section AAnswer all questions.

Section BAnswer any two questions.

In the event that all 3 questions are attempted, onlythe first 2 questions will be marked.

You are advised to spend about one hour on eachsection. Write your answers on this question booklet inthe blanks provided.

INFORMATION FOR CANDIDATES

The number of marks is given in brackets [ ] at the endof each question or part question. Marks will be

deducted if units are not stated where necessary or ifanswers are not quoted to the appropriate number ofsignificant figures.

All working for numerical answers must be shown.You are reminded of the need for good English andclear presentation of your answers.

Examiners Use

Section A

Q1 /5

Q2 /10

Q3 /10

Q4 /10

Q5 /5

Section B

Circle the questions youhave attempted

Q6 /20

Q7 /20

Q8 /20

Deductions

Total /80

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Preliminary Examination Meridian Junior College 20 September 2011JC2 H2 Physics 2011

2

DATA AND FORMULAE

Dataspeed of light in free space c = 3.00 x 108m s-1

permeability of free space o = 4 x 10-7 H m-1

permittivity of free space 0 = 8.85 x 10-12 F m-1

= (1/(36)) x 10-9 F m-1

elementary charge e = 1.60 x 10-19 C

the Planck constant h = 6.63 x 10-34 J s

unified atomic mass constant u = 1.66 x 10-27 kg

rest mass of electron me = 9.11 x 10-31 kg

rest mass of proton mp = 1.67 x 10-27 kg

molar gas constant R = 8.31 J K-1 mol-1

the Avogadro constant NA = 6.02 x 1023 mol-1

the Boltzmann constant k = 1.38 x 10-23 J K-1

gravitational constant G = 6.67 x 10-11 N m2 kg-2

acceleration of free fall g = 9.81 m s-2

Formulaeuniformly accelerated motion

s = ut +1

2at2

v2 = u2+2as

work done on/by a gas W = pV

hydrostatic pressure p = gh

gravitational potential = -Gm/rdisplacement of particle in s.h.m. x = xosin t

velocity of particle in s.h.m. v = vocos t

= 2 2o

-x x

resistors in series R = R1 + R2 +

resistors in parallel 1/R = 1/R1 +1/R2+

electric potential V = Q/4or

alternating current/voltage x = xosin t

transmission coefficient T

exp(-2kd)

where k =

2

2

8 ( )m U E

h

radioactive decay x = xo exp(-t)

decay constant =

1

2

0.693

t

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3

Section AAnswer all the questions in this section.

1 (a) Estimate the following quantities and provide the correct units: [3]

1. size of an atom = ..

2. speed of the fastest man on Earth = ..

3. power rating of a domestic light bulb = ...

(b) A micrometer screw gauge is used to measure the diameter of a copper wire. Thereading with the wire in position is shown in Fig. 1.1. The wire is removed and the jaws ofthe micrometer are closed. The new reading is shown in Fig. 1.2.

Determine the diameter of the wire.

Diameter= . mm [2]

Fig. 1.1 Fig. 1.2

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4

2 (a) State the first law of thermodynamics.

.

. [1]

(b) A mass of 1.00 kg of steam at a pressure of 1.01 105 Pa and temperature 100 oCoccupies 1.67 m3 and the specific latent heat of vaporization of water is 2.26 106 J kg-1.

Determine the difference between the internal energy of 1.00 kg of water and 1.00 kg ofsteam at a pressure of 1.01 105 Pa and a temperature of 100 oC. Density of water istaken 1000 kg m-3.

Internal energy difference = ................................ J [4]

(c) Use the kinetic model of matter to explain why evaporation of a liquid is accompanied bycooling, unless heat is supplied to the liquid.

...

...

...

[3]

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5

(d) State and explain how the rate of evaporation can be increased.

...

...

...

. [2]

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6

3 The figure below shows the schematic of a compact mass spectrometer onboard the MarsRover. The spectrometer comprises of a velocity selector placed within a uniform magneticfield of flux density, B = 0.100 T. Positive ions emerging from the velocity selector travelthrough a quarter of a circle to impinge upon a detector plate which is oriented at 45o to the

vertical. The electric field strength within the velocity selector is E= -150 kV m .

A sample of carbon is vaporized, ionized and fed into the spectrometer.

Fig 3.1

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7

(i) Show that the radius of the circular path undertaken by a positive ion emerging from thevelocity selector is:

2

mEr

qB=

[2]

(ii) Show that the time taken by a positive ion to hit the detector plate after leaving the velocityselector is:

2

mt

qB

=

[2]

(iii) The carbon sample contains both 12 13C and C isotopes. The isotopes are singly ionized i.e.

the ions have a charge of +e, and the mass of the ions are 261.99 10 kg and262.16 10 kg respectively,

1. Using the expression in 3(ii), calculate the time taken by the 12C ion to hit the detectorplate after leaving the velocity selector.

Time= . s [2]

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8

2. Using the expression in 3(i), calculate the radii of the circular paths taken by the12 13C and C ions.

12 CR = . m [1]

13 CR = . m [1]

3. Hence or otherwise, determine the distance on the detector plate, between the points ofimpact of the 12C and 13C ions.

Distance= . m [2]

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9

4 (a) Two coherent sources A and B of monochromatic light with wavelength are placed a distanceaapart as shown in Fig 4.1. They interfere at the wall situated a distance D away from thesources where D>>a. Sources A and B are in phase.

Fig 4.1

(i) When the light from A and B meets at P, a nth order bright fringe is obtained.

1. State the phase difference of A and B at P.

Phase difference = . [1]

2. State the path difference of BP and AP in terms of n, and a.

Path difference = . [1]

(ii) State the path difference for a mth order dark fringe in terms of m, and a.

Path difference = . [1]

(b) A student changed the set up in (a) by replacing the 2 sources with a single incident planewave on a diffraction grating. The incident plane wave has an equal mixture of red and bluelight only.

wavelength of red = 600 nmwavelength of blue = 400 nm

He observed a total of 9 colored fringes on the far wall and recorded their color and positions inFig 4.2. Carelessly, he forgot to record the color of fringe X on Fig 4.2.

nth order

doubleslit

screen

A

B

P

Oa

D

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10

Fig 4.2

(i) Suggest why the color of the central fringe is magenta.

.

. [1]

(ii) Suggest and explain quantitatively what the color of fringe X could be.

.

. [3]

(iii) Determine the minimum possible slit separation of the diffraction grating he used forFig 4.2.

slit separation = . m [3]

magenta fringe

blue fringe

red fringe

blue fringe

fringe X

fringe X

red fringe

blue fringe

blue fringe

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11

5 (a) Compare progressive and stationary waves in terms of

1. phase of all points within a wavelength

.

. [1]

2. energy transfer

.

. [1]

3. maximum kinetic energy of all particles within a wavelength

.

. [1]

(b) Give reasons for the observation:

Sound waves and water waves can go round corners but light waves seem to travel onlyin straight lines.

.

.

.

. [2]

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12

Section BAnswer two questions in this section.

(b) Two light chords suspend a non-uniform bar such that it is maintained at rest in ahorizontal position as shown in Fig. 6.1 below.

Fig. 6.1

By expressing TA in terms of TB, or otherwise, calculate the value of x, the position ofthe centre of mass of the rod measured from the left-hand end of the bar, given that the

mass of the bar is 1.0 kg.

x= .. m from the left end [4]

6 (a) State the conditions for an object to be at equilibrium.

.

.

.

. [2]

30.0

50.0

mg

x

6.5 mTBTA

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13

(c) (i) A bullet, with an effective cross-sectional area A, is travelling horizontally throughthe air with a speed v. As the bullet travels through the air, it will push a columnof air directly in front of it. The air column can be taken to be initially at rest.

Given that the density of air is , show that the magnitude of the force that the air

acts on the bullet at this instant is given by Av2. State clearly the laws applied inyour working. [3]

(ii) State and explain whether the above expression will accurately determine thedrag force of the air on the bullet in practical situations.

...

..

..

..

[2]

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14

(d) A bullet of mass 0.20 kg, travels horizontally and collides perfectly inelastically with asphere A of mass 4.0 kg, as shown in Fig. 6.2 (which is not drawn to scale).

Fig. 6.2

This causes A to move up the slope to a height of 0.30 m when it comes into contactwith a light spring of spring constant 10 kN m-1. A will further compress the spring by0.20 m before coming to an instantaneous stop. You may assume that the flat surfaceand the slope are frictionless.

(i) Determine the total mechanical energy of A and the bullet after the impact.

Total mechanical energy = .. J [3]

(ii) Determine the speed of A and the bullet immediately after the collision

Speed = m s-1 [2]

Fixed block

v

300

0.30 m

A

light spring

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(iii) Hence, determine the speed of the bullet just before the collision.

Speed = .. m s-1 [2]

(iv) Explain why A will experience a rise in temperature.

..

..

...

...

. [2]

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16

7 (a) (i) Explain why it is possible for gravitational field strength to be zero at a pointwhere the gravitational potential is not zero.

.

.

[2]

(ii) In the table below, indicate whether the change in electric potential energyincreases or decreases with increasing distance from the source charge.

Change in Electrical Potential Energy with increasingdistance from source charge

Negative test charge Positive test charge

Positive Source Charge

Negative Source Charge

[2]

(b) (i) ABC is a triangle in which AB = AC= BC = r. In Fig. 7.1, charges +Q and Q areplaced at A and B respectively.

Fig. 7.1

Draw the resultant electric field at point C in Fig. 7.1 and label it as ER. [1]

B

A

C

- Q

+ Q

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17

(ii) The charges are replaced by equal point masses placed at A and B.

Draw the corresponding resultant gravitational field at point C in Fig 7.2 and label

it as GR. [1]

Fig. 7.2

(c) (i) A space vehicle together with its booster stage initially joined together, move in a

circular orbit of radius Rabout the Earth. Assuming that Earth acts as a pointmass, show that the linear speed uof the combination is given by

R

GMu E=

where ME is the mass of the Earth. [2]

B

A

C

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(ii) The mass of the space vehicle is 2m and mass of booster is m. The spacevehicle and the booster in b(i) are separated by an internal explosion such thatthe booster and vehicle moves in opposite direction tangentially to the orbit. Theexplosion allows for the space vehicle to attain the escape speed necessary for itto just reach an infinite distance from Earth.

1. Show that the escape speed of the space vehicle is given by2 EGM

R

2. By considering conservation of momentum, determine the speed of thebooster in terms ofu immediately after the explosion.

Speed of the booster = . [3]

(iii) In terms of m and u, deduce an expression for the energy delivered by theexplosion as it separates the vehicle from the booster.[2]

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(d) A small conducting sphere of radius Rand mass m, is suspended from a very longinsulating thread between metal plates PP, xdistance apart. Plate P is at potential +Vwhile plate P is at potential V as shown in Fig. 7.3.

Fig. 7.3 (not drawn to scale)

After being given an initial displacement, the sphere moves to one of the plates, touchesit, then moves rapidly to the other, touches it and then moves to the opposite plateagain. This process repeats itself such that the sphere oscillates between the plates.

(i) Assume that the charge on the sphere behaves as if it were concentrated at thecentre of the sphere, show that the charge on the sphere when it is in contact with

plate P which has potential V, is given by .[2]

(ii) Deduce an expression for the acceleration of the sphere in terms of R, V,distance x between the metal plates and m, the mass of the sphere.(Assume that the effect of gravity is negligible).

[2]

S

P P

+V -V

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(iii) Show that the time taken for the sphere to move between P to P and back to P isproportional to x/V.

[3]

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8 (a) (i) Define the ohm.

...

. [1]

(ii) Two students argue over the claim that the equation V = I R, with student Aclaiming it is Ohms law, whilst student B disagrees.Discuss who is correct.

...

...

. [2]

(iii) A resistor is connected to a battery with negligible internal resistance, along withan ammeter and voltmeter, as shown in the circuit below. Assume the ammeter

and voltmeter are ideal. The reading on the voltmeter is 2.0 V.

Fig 8.1

By reference to energy conversion, distinguish what the 2.0 V represents1. across the battery and2. across the resistor.

1. Across the battery

...

2. Across the resistor

. [2]

V

A

2.0 V

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(b) A capacitor (symbol ) is a device that stores electrical energy through the

separation of charge. When a capacitor and an ammeter is placed in series with theresistor in the circuit below in Fig 8.2 and the switch closed, the ammeter reading isnoted to decrease with time, as shown in the graph Fig 8.3

As the capacitor charges, the potential difference across it builds up.

(i) Explain how the total charge that flows through the ammeter up to time tcan beobtained from the graph.

...

. [1]

(ii) Sketch and label, on the axis provided, the variation of potentialdifference, V across1. the resistor2. the capacitor [2]

Current

V

time

V

A

Capacitor Fig 8.2 Fig 8.3

time

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(c) The circuit in Fig. 8.4 belowhas a thermistor connected in series to a 10.0 k resistorand a 10 V battery of negligible internal resistance. Fig. 8.5 shows how the resistance,Rth, of the thermistor varies with temperature.

(i) A thermistor whose resistance falls as temperature rises is said to have aNegative Temperature Coefficient (NTC), and is normally made of asemiconducting material.Explain why the resistance of the component decreases as temperature rises.

...

...

. [2]

(ii) Calculate the current in the circuit when the temperature is 20 C

Current A [2]

(iii) Calculate the potential difference across the thermistor at 20 C

Potential difference = . V [1]

thermistor

10.0k

10 V

Fig. 8.4

Fig 8.5

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(iv) Calculate the power supplied by the battery at 20 C.

Power supplied = . W [1]

(v) A student suggests using another thermistor whose resistance varies from 10

to 100 in the same temperature range, and switching the 10.0 k resistance toa one of lower comparable resistance, reasoning that P=I

2R, so if resistance isdecreased, so will the power dissipated. Discuss whether the student is right orwrong.

...

...

. [2]

(v) The relationship between resistance, R/ and temperature, T/ K is given by

WhereTis the temperature in Kelvin, K.

Ris the resistance in Ohms, , at temperature TRo is the resistance value at a reference temperature To

is a constant, the temperature coefficient.

1. By substituting appropriate values obtained from the graph into the equation,

determine the value of the temperature coefficient, .

= . K [3]

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2. can be more accurately determined by plotting an appropriate linear graph anddrawing a best fit trend line. This method is more accurate as it allows us toreduce random error of each reading.

Suggest what graph to plot and identify how can be obtained from the graph.

.............

.............

[1]

End of Paper

mjc h2 phy p3

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