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H2 Physics 2012

Year 1 Revision (Part 2)

Source:

2010 Prelim Structured Questions &

JJC Promotional Exams (with solutions)

Please visit http://jjphysics.pbworks.com for

more questions or detailed solutions.

1. Current of electricity 2. DC circuit 3. Motion in a circle 4. Gravitational Field 5. JJ Promotional Exam

Papers I and II

(2008 to 2011)

http://jjphysics.pbworks.com/

H2 Physics/ 2012/ Year 1/ Revision/ Current of electricity Sources: 2010 Prelim Questions

1 Page

2010 RI H2 P3 Q2

1 (a) Distinguish between resistance and resistivity of a conductor.

[2]

(b) A cell of e.m.f. 2.50 V and internal resistance R is connected to two uniform resistive wires in

series as shown in Fig. 2.1. The wires are made of the same material but have different

lengths and diameters. Wire AB is 50.0 cm long and has a diameter d, whereas wire BC is

30.0 cm long and has a diameter 0.30 d. The ammeter and connecting wires are assumed to

have no resistance.

Fig. 2.1

Show that AB

BC

R

R 0.150

[2]

R

2.50 V

A B C

A


2 Page

(c) A battery of e.m.f. 2.00 V and internal resistance r is connected across wire BC in parallel

with another resistor of resistance r as shown in Fig 2.2. The galvanometer shows no

deflection when the jockey J is at the midpoint of wire BC.

Fig 2.2

(i) Show that VBC = 2.00 V [1]

(ii) Determine the internal resistance R of the 2.50 V cell if the ammeter shows a reading of

0.400 A.

R = [3]

(d) Suggest and explain whether your answer in part (c)(ii) is an over-estimate or under-

estimate if the ammeter is not ideal.

[2]

R

2.50 V

A B C

r

r

2.00 V

A

J


3 Page

2010 RVHS H2 P2 Q5

2 (a) Distinguish between electromotive force and potential difference.

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………… [2]

(b) An electric hotplate is designed to operate on a power supply of 240 V has two coils of wire of

resistivity of 9.8 10–7

m. Each coil of wire has a length of

16 m of cross-sectional area 0.20 mm2.

(i) For one of the coils, calculate

1. its resistance,

resistance = …………………………

2. the power dissipation when a 240 V supply is connected across it.

power = ………………………… W [4]


4 Page

(ii) Fig. 5.1 shows how the two coils can be connected to operate at different powers.

Fig. 5.1

On Fig. 5.2, fill up the table with “ON” or “OFF” to obtain the lowest and highest

levels of operating power. [2]

switch A switch B switch C

Lowest

Highest

Fig. 5.2

2010 VJC H2 P2 Q6

3 A wire-wound resistor is manufactured by winding resistance wire on an insulating former. A

commonly used material for the wire is an alloy of nickel and chromium called nichrome. The wire

is produced by pulling the nichrome through a suitable sized hole. Nichrome is sufficiently ductile

to be drawn into a wire without danger of it cracking or breaking after winding. It resists corrosion

and has a fairly high resistivity. The wire itself must be uniform and thin, and is covered with an

insulating material.

A manufacturer of resistors of this type supplies information concerning them in the form of a

family of lines shown in the graph of Fig. 6. Resistors of different resistance R1, R2, … R5 etc are

shown by the separate lines.

(a) By choosing some values of potential difference and current from Fig. 6, complete the table

showing the resistances R1, R2, … R5. [2]

240 V

A

B C


5 Page

Fig. 6

R1 =

R2 =

R3 = 1000

R4 =

R5 =

(b) Draw two additional lines on Fig. 6:

(i) one line for a resistance of 2000 ,

(ii) one line for a resistance of 47 . [3]

(c) This particular set of resistors is manufactured so that the resistors can safely be used with power

dissipation up to 1 W. Complete the following table to show the maximum safe current in the

resistors for the potential differences given. [2]

(d) Plot the points in (c) on the graph of Fig. 6. On the graph, indicate the region of safe use for all

these resistors. [4]

Potential difference / V Maximum current / A

1000

100

10

1


6 Page

(e) The lines on Fig.6 represent ideal behaviour. Suggest, with a reason, how the line for a real resistor

might differ from the ideal. [2]

2010 VJC H2 P3 Q4

4 (a) Define resistance and the ohm.

[2]

(b) A wire with a resistance of 6.0 Ω is stretched so that its new length is three times

its original length. Assuming that the resistivity and density of the material are not

changed during the stretching process, calculate the resistance of the longer wire.

[3]

(c) The circuit shown in Fig. 4 is constructed of resistors, each of which has a

maximum safe power rating of 0.40 W.

(i) Find the maximum potential difference that can be applied between X and

Y without damage to any of the resistors.

[3]

Fig.4

X

Y

160

1000

1000


7 Page

(ii) If this potential difference were exceeded, explain which resistor would be

most likely to fail.

[2]

2010 TPJC H2 P2 Q3

5 (a) Define potential difference and the volt. [2]

(b) The variation of resistance R of a thermistor with temperature T is shown in Fig.

3.1.

The above thermistor is connected in a potential divider circuit as shown in Fig. 3.2 with a battery of e.m.f.

12.0 V and negligible internal resistors. The thermistor is placed in the freezer of a meat handling factory. It

functioned as a temperature probe to activate a switch to power the freezer and the switch will be on if the

potential at point P is at 4.5 V.


8 Page

(i) What is meant by the expression an e.m.f. of 12 V ? [1]

(ii) State and explain the effect of a decrease in surrounding temperature in the freezer on the potential at

point P. [3]

(iii) Use Fig. 3.1 to determine the temperature that would trigger the switch.

temperature = …………………………….. K [3]

(iv) Suggest why it is reasonable to choose a value of 4.5 V as a trigger potential in this context. [1]

(v) Without changing the thermistor and keeping the trigger potential at 4.5 V, suggest one way that the

circuit could be modified if a different trigger temperature is desired. [1]


9 Page

(vi) Noting the usefulness of such a temperature probe, it was suggested that a similar circuit in Fig. 3.2 to be

used in a device for controlling a boiler. It is desired that when the temperature is 78oC, the switch will

be activated to boil the liquid. Discuss whether this proposal is feasible. [2]

2010 ACJC H2 P2 Q4

6 You are tasked to investigates how the current through a 6.0 V filament lamp varies as the potential

difference across it is changed up to 6.0 V. You are supplied with the following apparatus: a rheostat, a

9 V cell, an ammeter, voltmeter and connecting wires

(a) Draw a suitable circuit diagram for this investigation using only the above given apparatus.

[2]

(b) (i) Use the axes below to sketch the graph showing how the current through the lamp varies

with the potential difference across it. [2]

(ii) Justify the shape of the graph.

[2]

Current

Potential difference


10 Page

(iii) Explain how your graph shows that the resistivity of the filament is unique at a specific

temperature.

[1]

2010 JJC H2 P2 Q2

7 A small electric torch is powered by a single cell which supplies 1.6 J of energy per coulomb of

charge passing through the cell. When the torch is switched on, the cell supplies a constant

current of 0.50 A to bulb X. The potential difference across the bulb is 1.2 V.

(a) Show that the internal resistance, r, of the cell is 0.80 Ω. [2]

(b) The bulb X, is replaced by another bulb Y, which is found to take a current of 0.30 A.

Calculate the

(i) new potential difference across the internal resistance of the cell, [1]

(ii) the potential difference across bulb Y. [1]

(c) By considering their power usage, calculate the power lost in the cell for each of the cases

when connected to bulb X and to bulb Y. [4]


11 Page

2010 MI H2 P3 Q3

8 (a) In Fig. 3.1 below, the battery has an internal resistance r and the ammeter has negligible

resistance.

Fig. 3.1

The graph in Fig. 3.2 below shows how current I in the circuit varies as the potential

difference V across the variable resistor R changes.

Fig. 3.2

(i) Define the term potential difference.

……………………………………………………………………………………………

……………………………………………………………………………………………

………………………………………………………………………………………...[2]


12 Page

(ii) 1. Show that the e.m.f E of the battery is 6 V. [2]

2. What is the power dissipated in the variable resistor R when the current in the circuit is 1.2 A?

power dissipated =……………..W [2]

3. What is the internal resistance r of the cell?

internal resistance r =……………… [2]

(b) Four resistors are connected as shown in Fig. 3.3 below. Point a is at a higher potential than

point b.

Fig. 3.3

If a wire is connected from c to d, state and explain the direction of the current that will flow

through the wire.

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

………………………………………………………………………………………………[2]


13 Page

2010 MJC H2 P3 Q3

9

(a) A thin layer of copper is deposited uniformly on the surface of an iron wire of radius 0.60

mm and length 3.0 m shown in Fig. 3.1.

Fig. 3.1 (Not to scale)

Determine the effective resistance between the ends of the copper-plated wire, given that

the thickness of the copper is 1.78 x 10-5

m.

[Resistivity of iron = 8.90 x 10-8

Ω m; resistivity of copper = 1.60 x 10-8

Ω m]

effective resistance = .......................... Ω [3]

(b) Fig. 3.2 shows a system in which an unmodulated audio frequency signal is transmitted

from the transmitter to the receiver through a cable. The cable consists of two strands of

insulated copper wire.

Fig. 3.2

The power output of the transmitter is 12.5 mW and the corresponding current in each wire

is 2.5 mA. Power is lost to the surroundings due to the rise in temperature produced by this

current. For transmitted signal to be detected the power input to the receiver must be at

least 1.5 mW.

The resistance of each 1.0 m of the copper wire used in the cable is 0.27 Ω.

Calculate the maximum distance between the transmitter and receiver at which the

transmission can be detected successfully.

I

insulation

transmitter 12.5 mW

receiver

copper wire

iron wire

thin layer of copper

I


14 Page

maximum distance = ……………………m [3]

2010 AJC H2 P3 Q7

10 (a) (i) Define, in the context of an electrical circuit, the following,

Coulomb

Joule

Watt

(ii) Based on your answers in (a)(i), hence, show the units for potential difference in terms of SI base

units. [2]

(b) A car headlamp is marked 12 V, 72 W.

(i) Calculate the working resistance of the car headlamp.


15 Page

(ii) The lamp in (b)(i) is connected to a battery of e.m.f. of 12 V with an internal resistance of 0.20 Ω as

shown in Fig 7.1.

The car headlamp is switched on for a 20 minute journey.

Using your answer in (b)(i), calculate the current in the lamp.

1. the charge which passes through the lamp during the journey,

2. the energy supplied to the lamp during the journey.

(c) Two of the headlamps referred to in (b) are connected into the circuit shown in Fig 7.2, in which one

source of e.m.f. (generator of the car) is placed in parallel with the car battery and the two lamps. Both lamps

are on and are working normally.

The battery has an e.m.f. of 12.0 V and an internal resistance of 0.20 Ω. The generator has an e.m.f. of 15.0

V and negligible internal resistance. The generator is in series with a variable resistor R.


16 Page

(i) The value of R is adjusted so that there is no current in the battery when the lamps are on. Calculate

1. the current in the generator,

2. the value of the resistance of R.

(ii) Calculate the current in the battery when both lamps are switched off, the value of R

remaining the same as in (i).

(d) Suggest two advantages which the circuit, as shown in Fig 7.2, has over a single power source.

END

H2 Physics/ 2012/ Year 1/ Revision/ D.C circuits Sources: 2010 Prelim Questions

1 Page

2010 NYJC H2 P3 Q3

1 Fig 3.1 shows a circuit for measuring a small e.m.f. produced by a solar cell.

(a) The galvanometer shows null deflection when the variable resistor is set to 300 Ω. Determine

the value of the e.m.f., V of the solar cell.

V = V [2]

(b)

10 V

Solar cell

V

5.0

0.5

Fig 3.1

0.5

10 V

Solar cell

V

P

moveable

contact R

Q

I

Fig 3.2


2 Page

(i) Calculate the current I, when the galvanometer shows null deflection

I = A [2]

(ii) Calculate the distance from P that contact R must be connected to wire PQ such that the

galvanometer shows null deflection.

Distance from P = m [3]

(iii) Explain why, this circuit is not suitable for measuring the e.m.f. of the solar cell when the

value of the e.m.f. of the solar cell is of the order of millivolts.

[1]

2010 PJC H2 P3 Q3

2 Fig. 3.1 shows a potential divider arrangement using a fixed resistor of resistance 4.0 kΩ and a variable

resistor of maximum resistance 20 kΩ with a slide contact connected to terminal S.

Fig. 3.1

20 kΩ

4.0 kΩ

12 V

X

Y

Z

S


3 Page

The e.m.f. of the battery is 12 V and it has negligible internal resistance. It is possible to obtain different

continuously-variable ranges by selecting, as the output, particular pairs of terminals from S, X, Y and Z.

(a) (i) Calculate the voltage range obtainable between the terminals S and X.

voltage range = .................V to................... V [2]

(ii) Hence, or otherwise, calculate the voltage range between the terminals S and Z.

voltage range = .................V to................... V [1]

(b) The slide contact S is set at the mid-point of the 20 kΩ resistance track. A voltmeter of resistance of 10 kΩ is then connected between S and Y. Calculate the reading on the voltmeter.

voltmeter reading = ........................................ V [3]


4 Page

(c) The variable resistor in Fig. 3.1 is replaced by a thermistor T, as shown in Fig. 3.2. At room

temperature, the resistance of the thermistor is 12 kΩ. When it is placed in hot liquid, its resistance

falls to 2.0 kΩ.

Fig. 3.2

(i) On Fig. 3.3, sketch the temperature characteristic of the thermistor.

Fig. 3.3

[1]

(ii) Using the band theory, explain the variation of the thermistor’s resistance with temperature.

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

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

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

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

[3]

4.0 kΩ

12 V

X

Y

Z

T

resistance / Ω

temperature / °C 0


5 Page

2010 SAJC H2 P3 Q4

3 (a) Fig. 4.1 shows a cell of e.m.f. 2.0 V and internal resistance 0.20 connected in parallel to

two identical lamps L1 and L2. The ammeters A1 and A2 in the circuit have negligible

resistance and A2 reads 0.50 A.

(i) Calculate the potential difference across L1.

potential difference = …………V [2]

(ii) If another identical lamp L3 is connected in parallel with L1 and L2, explain whether

the current in ammeter A1 remains the same, increases or decreases.

…………………………………………………………………………...

…………………………………………………………………………...

…………………………………………………………………………...

…………………………………………………………………………...

……………………………………………………………………….[2]

Fig. 4.1

2.0 V

0.20

A1

L1

A2

L2


6 Page

(b) Fig. 4.2 shows a circuit which is used to measure the emf of Cell Y.

Cell X has an e.m.f. of 2.00 V and negligible internal resistance. It is connected in series with

a 8.0 resistor and resistance wire AB. The resistance wire AB has a length 100.0 cm and a

resistance, 2.0 .

(i) Calculate the potential difference across AB.

potential difference = …………V [1]

(ii) The movable contact J is now moved along AB. When the galvanometer indicates a

zero reading, the length AJ is 30.0 cm. Calculate the e.m.f., in mV, of Cell Y.

e.m.f.= ……..….. V [2]

Cell Y

B A J

8.0

Cell X, 2.00 V

Fig. 4.2


7 Page

(iii) Without changing the length AB, suggest three modifications to the circuit of Fig. 4.2

that would cause the contact J to be closer to A when the galvanometer gives a zero

reading.

1. ………………………………………………………………………..

………………………………………………………………………..[1]

2. ………………………………………………………………………..

………………………………………………………………………[1]

3. ………………………………………………………………………..

………………………………………………………………………[1]

2010 TJC H2 P2 Q7

4 The ex In an experiment to investigate the light emitted by a filament lamp, the light output for a

lamp rated at 12 V, 20 W was investigated when a range of potential differences was applied

across it.

(a) When the lamp is operating normally, calculate

(i) the current in the lamp;

current = A

[2]

(ii) the resistance of the filament.

resistance = [1]


8 Page

(b) Draw a circuit diagram showing how you would connect the lamp to a 12 V battery and

a 10 Ω rheostat such that the potential difference across the lamp can be varied between

0 and 12 V.

Include in your diagram:

- a switch, situated so that the battery supplies no current when the switch is open; - a voltmeter and an ammeter, which will enable the power supplied to the lamp to be

determined.

[3]

(c) The lamp drawn in (b) is now used to illuminate the LDR as shown in Fig. 7.1.

The LDR is then connected to a circuit as shown in Fig. 7.2 where it is used in

investigating the intensity of the light output of the lamp. The battery in the circuit is

assumed to have negligible internal resistance and the milliammeter has a full scale

deflection of 10 mA.

The graph in Fig. 7.3 shows how the resistance R of the LDR varies with the incident

illumination L, which is measured in W m-2

. Both resistance and illumination are

plotted using log10 scales.

LDR

in Fig. 7.2

Fig. 7.1 Fig. 7.2


9 Page

(i) To enable maximum use of the available illumination range, a full scale

deflection of the milliammeter is required when the lamp is operating at

maximum brightness. Explain the steps you would take in order to obtain this

initial condition.

[2]

(ii) Calculate the minimum resistance of the LDR when the milliammeter is at its full

scale deflection.

minimum resistance = [2]

Log10 (L/Wm-2) 0 1 2 3 4

1

2

3

4

0

Fig. 7.3

Log10 (R/) 5


10 Page

(iii) Use Fig. 7.3 to show that the maximum illumination which can be measured,

using the circuit shown in Fig. 7.2, is about 1000 W m-2

.

[2]

(iv) If the uncertainty of the milliammeter is 0.5 mA, determine whether there is a

detectable current when the illumination is 10 W m-2

.

[3]

2010 YJC H2 P2 Q2

5 Fig. 2.1 shows a potentiometer circuit that can be used to determine the unknown e.m.f. of a test cell.

The driver cell has an e.m.f. of 12 V and internal resistance of 1.5 Ω. The resistance of the rheostat can

vary between 0.0 Ω and 5.0 Ω and the resistance wire has a length of 1.2 m.

(a) When the resistance of rheostat is 2.3 Ω, the balance length is 0.57 m. When the resistance of

rheostat is changed to 3.5 Ω, the balance length becomes 0.68 m. Calculate the e.m.f. of the test cell

and the resistance of the 1.2 m long resistance wire.

[4]

Fig. 2.1

12 V, 1.5 Ω

Test cell

0.0 – 5.0 Ω

1.2 m long resistance wire


11 Page

Emf of test cell = ……………….. V

Resistance of 1.2 m long resistance wire = ……………….. Ω

(b) State what will happen to the balance length if the internal resistance of the test cell is doubled.

[1]

………………………………………………………………………………………

(c) Explain why the resistance of the rheostat cannot be higher than a particular value, if the

potentiometer is to be able to determine the unknown e.m.f.

[2]

………………………………………………………………………………………

………………………………………………………………………………………

2010 YJC H2 P2 Q5

6 (a) A heating device is designed to operate on either an a.c. or d.c. power supply. The device has a resistance

of 6.0 . Calculate the average power dissipated in the device when operating at

(i) an a.c. supply of voltage 12.0 V, 50 Hz

average power dissipated = …………. W [2]


12 Page

(ii) a d.c. supply of voltage 12.0 V

average power dissipated = …………. W [1]

(b) Draw the time t variation of the power P dissipated in the device for both the a.c. and d.c. supply on the

same axes below. Mark values on both axes.

[4]

(c) The alternating supply of voltage 12.0 V, 50 Hz is derived from the mains supply of voltage 230 V, 50

Hz using a transformer, assumed to have 100% efficiency.

Calculate the primary r.m.s. current when the heating device is in use.

primary r.m.s. current = …………….. A [2]

P / W

t / s


13 Page

2010 JJC H2 P3 Q3

7. (a) A battery of e.m.f 6.0 V is connected to a lamp and a high resistance voltmeter as

shown in Fig. 3.1.

(i) When the switch S is closed, the lamp lights up and the reading on the voltmeter

is 5.6 V. Explain why the reading is less than the e.m.f of the battery. [1]

(ii) The brightness of the lamp can be adjusted with a variable resistor that is

connected parallel to AB.

1. Explain qualitatively why the brightness varies. [2]

2. Several lamps are needed in a house and the lamps are connected in parallel

instead of in series to the mains. Suggest one advantage in this arrangement.[1]

V 6.0 V

Fig. 3.1

B

A S


14 Page

(b) Fig. 3.2 shows a simple series circuit connected to a potentiometer which consists of

a battery, a variable resistor and a uniform slide-wire of length L. The balance length,

LY, is achieved by sliding the key along the slide-wire till the galvanometer shows a

null deflection.

Fig. 3.2

(i) Explain how an increase in the resistance of the variable resistor will affect

the magnitude of LY. [2]

(ii) The galvanometer is now removed from Y and connected to X. A balance

length of Lx is found by sliding the key along the slide-wire till the

galvanometer shows a null deflection. Find the ratio of LX : LY. [2]

6 V

R 2R 3R

LY

X Y

Sliding key

12 V


15 Page

2010 NJC H2 P3 Q4

8 (a) Define the ohm. [2]

(b)(i) The figure below shows a potentiometer setup where the potentiometer wire, ab, is

uncalibrated. Es is a known standard cell. Describe how it is used to measure the emf

of the unknown source x .

[2]

(ii) Discuss one advantage of using the potentiometer setup to measure the emf Ex.

[1]

Es

G

E

Ex switch

a c b


16 Page

(c) The potentiometer wire ab of length 1 metre has a resistance of 600 . The rheostat,

R, has a resistance 400 for the entire length of 50 cm. The previous circuit has been

altered as follows:

(i) Determine the balance length, ac. [2]

(ii) State the direction of the current flowing through the dry cell, Ex, when the rheostat R

is adjusted from the midpoint to the right at the 40 cm mark. [1]

(iii) Find the new balance length, ac’. [2]

G

E = 5.0 V

Ex = 2.0 V

a c b

Rheostat, R = 400

midpoint 0 cm 50 cm

r = 10

ac = ……………….. m

ac’ = ……………….. m


17 Page

M

2010 CJC H2 P2 Q5

9 (a) A set of coloured lamps are designed for use with a 240 V supply. The set up have 12 lamps

connected as seen in Fig 5 below.

Fig. 5

However, the lamps do not light up when the set is plugged in. Therefore, a voltmeter is used

to test the circuit. For each of the following observations, identify the fault.

(i) The potential difference is zero across every lamp except EF, across which the

potential difference is 240 V.

……………………………………………………………………………………………

……………………………………………………………………………………………

[1]

(ii) The potential difference between A and M is 240 V but the potential difference is zero

across every lamp.

……………………………………………………………………………………………

……………………………………………………………………………………………

[1]

(b) (i) Some lamps are designed so that when the filament fails the resistance of the lamp

drops to zero. If this happens to one of the lamps in the above set up, calculate the

fractional increase in the power dissipated in each of the remaining lamps, assuming

that the resistance of these lamps does not change.

Fractional increase = _______________

[4]

(ii) What is likely to happen if failed lamps are not replaced?

……………………………………………………………………………………………

240 V a.c.

A B C D E F G H I J K L


18 Page

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

[2]

2010 AJC H2 P2 Q5

10. Fig. 5.1 shows a potential divider circuit consisting of two resistors with resistances 10 kΩ and 40 kΩ

respectively. The battery has an e.m.f. E and negligible internal resistance.

a. Determine the potential difference VWX across the 10 kΩ resistor in terms of E.

b. A thermistor P is connected in parallel with the 10 kΩ resistor and a resistor of resistance 20 kΩ is connected in parallel with the 40 kΩ, as shown in Fig. 5.2.

A galvanometer is connected between X and Y. At room temperature of 29 °C, it was found that there is no

current flowing through the galvanometer.


19 Page

i. Suggest what can be deduced about the potential at points X and Y at 29 °C.

ii. Determine the resistance of the thermistor P at 29 °C.

iii. The temperature of the thermistor is slowly raised.

1. Indicate on Fig 5.2 the direction of the current flowing between X and Y.

2. Explain why a reading is detected on the galvanometer whenever the temperature is not at 29 °C.


20 Page

2010 SRJC H2 P2 Q6

11 Fig. 6.1 shows a circuit in which PR is a 20.0 Ω slide wire, 75.0 cm long. E2 is a 40.0 V cell. Both E1

and E2 have non-negligible internal resistance. R1 and R2 are resistances of 8.0 Ω and 5.0 Ω

respectively.

The balance length is 60.0 cm when S1 and S2 are open as shown in Fig 6.1.

(i) When E1 is replaced with a 12 V cell with negligible internal resistance, the balance length becomes 45.0

cm. Calculate the internal resistance of the E2.

(ii) Calculate the electromotive force of cell E1

(iii) Calculate the balance length when S1 and S2 are closed. It is given that the internal resistance of E1 is

3.0 Ω

END

H2 Physics/ 2012/ Year 1/ Revision/ Motion in a circle Sources: 2010 Prelim Questions

1 Page

2010 SAJC H2 P2 Q3

1 (a) The Earth may be considered to be a uniform sphere of radius 6370 km, spinning on its axis

with a period of 24.0 hours.

(i) Calculate the angular velocity of a 2.00 kg mass situated at the equator.

angular velocity = …………rad s-1

[1]

(ii) At the North Pole, an accurate spring balance supporting the 2.00 kg mass gives a

reading of 19.66 N. What is the reading on the spring balance if the measurement is

taken at the equator?

force = ………..N [2]

(iii) Explain the difference (if any) in the readings of the spring balance in (a) (ii).

………………………………………………………………………......

………………………………………………………………………......

..……………………………………………………………………….[1]


2 Page

(b) An astronaut in a spacecraft orbiting the Earth may be described as weightless. Explain why

this is so.

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

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

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

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

…………………………………………………………………………..........[2]

2010 TJC H2 P3 Q5a, 5b

2 (a) Use Newton’s laws of motion to explain why a body moving with uniform speed in a

circle must experience a force towards the centre of the circle.

[2]

(b) A small mass m and a heavy mass M are connected to the ends of an inextensible string.

The string is threaded through a glass tube as shown in Fig. 5.1. The tube is then held by

a student and is whirled so that the mass m rotates with a constant radius r at a frequency

of 180 revolutions per minute. Given that m = 0.10 kg and M = 1.0 kg.

(i) Calculate the tension in the string.

tension =

N

[1]

m

M

r

Fig. 5.1


3 Page

(ii) Calculate the resultant force acting on the mass m.

resultant force on mass m = N [2]

(iii) Hence calculate the radius r of the circle.

r =

m

[2]

(iv) Explain whether it is possible for the small mass m to be whirled in such a

way that the string attached to it becomes horizontal.

[2]

2010 YJC H2 P3 Q3

3 In the recently opened Universal Studios, one of the roller coaster sections includes a loop-a-loop

that looks like the one shown in Fig. 3.1. The radius of the loop is 18.0 m and the centre of the loop

is 20.0 m from the ground.

Fig. 3.1

18.0 m

20.0 m

Coaster car


4 Page

(a) If the mass of a coaster car is 250 kg and there is no support system holding the car to the

track, calculate

(i) the minimum speed at the top of the loop required for the car to stay in contact with

the track, [2]

Minimum speed at the top of loop = ………………….. m s−1

(ii) the minimum speed the car needs to have when it enters the loop, if the car loses 15.0

J of energy per unit length of track travelled, and[3]

Minimum speed when entering loop = …………………… m s−1

(iii) the vertical force exerted by the track on the car when the car just enters the loop.

[2]

Vertical force exerted by track = ………………….. N


5 Page

(b) Explain why is the magnitude of the force calculated in (a) (iii) not equal to the weight of the

car.[1]

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

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

2010 MI H2 P3 Q2

4 (a) State the formula to calculate the centripetal force required to keep a body of mass m,

moving in a circle of radius r with speed v.

…………………………………………………………………………………………

………………………………………………………………………………………[1]

(b) A smooth toy car track is set up in the following manner as seen in Fig. 2.1 below.

Fig. 2.1

Cars 1 and 2 are identical in construction and have a mass of 500 g each. Car 1 is

released from rest at point A, which is at a height of 0.60 m. Car 1 is designed to

move down the slope and complete the circular loop (during which it would be upside

down at the top of the loop), before colliding with Car 2.


6 Page

(i) Calculate the speed of Car 1 at point B after it has moved down the slope.

speed of Car 1 at point B =………………….. m s-1

[2]

(ii) If Car 1 was to just reach point C, i.e., it comes to a complete stop at point C,

state the height of the circular loop.

height of circular loop =……………… m [1]

(iii) Explain why if the circular loop has the height that is calculated in (b) (ii), Car

1 would be unable to complete the entire loop safely.

………………………………………………..…………………………………

………………………………………………………..…………………………

…………………..…………………………………….……………………[2]

(iv) Hence or otherwise, calculate the maximum radius of the circular loop.

maximum radius of circular loop =………………m [2]


7 Page

(c) After completing the loop, Car 1 collides elastically with Car 2. Car 1 comes to a

complete stop, and Car 2 moves forward and compresses the spring until it comes to

a complete stop

Given that the spring constant of the spring is 150 N m-1

, calculate the compression of

the spring when Car 2 comes to a complete stop.

compression of spring =……………… m [2]

2010 NJC H2 P3 Q1

5 (a) Define the term angular velocity. [1]

(b)(i) A 10 kg baggage is left on a rotating baggage carousel at an airport. The baggage stays

at a fixed position on the slope of the carousel and rotates about in a circle

(r = 11.0 m) at a constant speed. The frictional force acting on the suitcase is 59.4 N.

Use Newton’s Laws to explain why the baggage will experience a net force towards the

centre of the circle. [2]

r

= 36.0º

Side View

Direction of rotation


8 Page

(ii) Show on a fully labelled diagram the forces acting on the baggage. [2]

(iii) Considering the forces acting on the baggage in the vertical direction, show that the

normal contact on the baggage is about 78.1 N. [2]

(iv) How much time is required for the suitcase to complete one full rotation? [3]

Time taken = ………………..


9 Page

2010 SRJC H2 P2 Q3

6 A pendulum bob is tied to a string as shown in Fig. 3.1. A person swings it in a vertical circular path. The

mass of the bob is 45.0 g. The length of the string is 70.0 cm. The diameter of the bob is 2.0 cm.

(i) Calculate the range of angular speeds to achieve this motion.

(ii) Calculate the maximum tension experienced in the string when the bob is spun at an angular speed of

5.00 rad s-1

.

(iii) State the assumption made in your calculation in part (ii).

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

……………………………………………………………………………………………..……[1]

(iv) Explain what might happen to the pendulum bob if it is spun around at an increasing angular speed.

END

H2 Physics/ 2012/ Year 1/ Revision/ Gravitational Field Sources: 2010 Prelim Questions

1 Page

2010 NYJC H2 P3 Q2

1 (a) Define gravitational field strength and gravitational potential.

[2]

(b) A point S is located between the Earth and the Moon at a distance r from the Earth along on the

line joining the centres of the Earth and the Moon.

The distance from the centre of the Earth to the centre of the Moon is 3.8 x 108 m, the mass of

the Earth is 6.0 x 1024

kg and the mass of the Moon is 7.0 x 1022

kg.

Find the value of distance r, if S is the point where the resultant gravitational field strength is

zero.

r = m [2]

(c) Sketch a graph (without any values) showing the variation of gravitational field strength with

distance from the Earth, along the line joining the Earth and the Moon.

[2]


2 Page

(d) Explain why a space craft would require more energy to move from the Earth to the Moon compared

to the return journey from the Moon back to the Earth. [2]

2010 PJC H2 P3 Q5

2 (a) The value of the gravitational potential at a point in the Earth’s field is given by the

equation

r

GM

where M is the mass of the Earth and r is the distance of the point from the centre of the Earth such

that r is greater than the radius of the Earth ER .

(i) Define gravitational potential at a point.

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

........................................................................................................................... [1]

(ii) Explain why the potential has a negative value.

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

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

........................................................................................................................... [1]


3 Page

(b) Fig. 5.1 shows the equipotential lines for Earth, where point A is at a potential of 7100.4 J kg−1

and points B and C are at a potential of 7100.5 Jkg−1

.

Fig. 5.1

(i) On Fig. 5.1, draw the equipotential line for the gravitational potential of 7105.4 Jkg−1

. [1]

(ii) Calculate the work done by the gravitational field in bringing a body of mass 3000 kg from A to

B.

work done = ........................................ J [2]

(iii)The work done by the gravitational force in bringing the mass from B to C along the

equipotential line is zero. Explain why this is so.

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

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

........................................................................................................................... [1]

7100.5 Jkg−1

7100.4 Jkg−1

Earth

A

B

C


4 Page

(c) (i) Show that a body projected from the Earth’s surface (assumed stationary) with a speed equal to

or greater than the escape speed EgR2 will never return. State any assumption(s) made in your

workings for this result to be valid.

[3]

(ii) Information related to the Earth and the Sun is given below.

5103.3Earthofmass

Sunofmass

110Earthofradius

Sunofradius

Given that the escape speed from the Earth is 4101.1 ms−1

, calculate the escape speed from the

Sun.

escape speed = ........................................ ms–1

[2]

(iii) The surface temperature of the Sun is about 6000 K and hydrogen is the most abundant element

in the Sun’s atmosphere. Explain why this is so by means of suitable calculations, assuming that

hydrogen is an ideal gas.

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

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

........................................................................................................................... [2]


5 Page

(d) Fig. 5.2 shows the way in which the gravitational potential energy of a body of mass m depends on r.

Fig. 5.2

(i) What does the gradient of the tangent to the curve at ERr represent?

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

........................................................................................................................... [1]

(ii) The body is projected vertically upwards from the Earth’s surface. At a certain distance R from

the centre of the Earth, the total energy of the body may be represented by a point on the line XY.

Five points, A, B, C, D, E have been marked on this line.

Explain clearly which point(s) could represent the total energy of the body

1. if it were momentarily at rest at the top of its trajectory,

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

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

........................................................................................................................... [2]

2. if it were falling towards the Earth,

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

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

energy

r

tangent

potential energy

R ER

A

B

X

C

D

E

Y


6 Page

........................................................................................................................... [2]

3. if it were moving away form the Earth, with sufficient energy to reach an infinite distance?

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

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

........................................................................................................................... [2]

2010 RI H2 P2 Q3

3 (a) Gravitational field strength g and gravitational potential at a point due to a spherical

body are related by the equation gr

d

d

where r is the distance from the centre of

the body to the point. Explain the significance of the negative sign.

[1]

(b) Given the mass of Earth is 5.98 x 1024

kg and its radius is 6370 km, determine the

minimum kinetic energy required to project a spacecraft of mass 2550 kg from the

surface of Earth so that it completely escapes from the gravitational field of Earth.

Ignore air resistance.

Minimum energy = J [3]

(c) As a spacecraft falls towards Earth, it loses gravitational potential energy. State the

energy conversions for the spacecraft when it is falling through Earth’s atmosphere at

constant speed.


7 Page

[1]

(d) An astronaut in a spacecraft orbiting around Earth can be said to experience

weightlessness. Explain why this is not true weightlessness.

[2]

2010 RVHS H2 P3 Q5

4 (a) Define gravitational potential at a point in a gravitational field and state its unit.

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………… [2]

(b) Fig. 5.1 shows the variation of gravitational potential between the surface of Moon and

the surface of Earth along the line joining the centres.

Fig. 5.1

The following data is required in answering the question.

P

X

Moon

Earth

– 62.3

potential/106 J kg–1

– 3.9

– 1.3

Y


8 Page

mass of the Earth 5.98 1024

kg

mass of the Moon 7.35 1022

kg

distance from the centre of the Moon to the centre of the

Earth 3.84 10

8 m

(i) State how the resultant gravitational field strength can be deduced from Fig.

5.1.

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

……………………………………………………………………………… [2]

(ii) State the gravitational field at point P.

……………………………………………………………………………… [1]

(iii) Hence, or otherwise, determine distance X.

distance X = ………………………… m [3]

(iv) A rocket of mass 2.7 106 kg on a mission to the Moon is to be launched from

Earth. In order to reach the surface of the Moon, the rocket must be launched

with a minimum speed.

1. Using Fig. 5.1, determine this minimum speed. Explain your working

clearly.

[4]


9 Page

2. With this minimum speed, calculate the speed at which the rocket will land

on the Moon’s surface.

landing speed on the Moon = ………………………… m s–1

[2]

(c) The Moon is a natural satellite of the Earth. It can be assumed that the Moon travels at a

constant speed around the Earth in a circular path, with the Earth at the centre of the

circle.

(i) Using Newton’s laws of motion, explain why an object travelling in a circle with

constant speed has an acceleration. State the direction of this acceleration.

……………………………………………………………………………………

……………………………………………………………………………………

……………………………………………………………………………………

……………………………………………………………………………… [3]

(ii) Show that orbital period T of a satellite and its distance r from the Earth is given

by

32

2 4 rGM

TE

where G is the gravitational constant, ME is the mass of the Earth.

[3]


10 Page

2010 SAJC H2 P2 Q7

5 For thousands of years, Man has studied the night sky and some ancient buildings provide evidence

of careful and patient astronomical observations by people of many different cultures. As

instrumentation has improved, so has the precision with which astronomical observations could be

made. Between 1576 and 1597, Brahé made comprehensive observations of planetary positions and,

on his death, these records became available to Kepler.

Kepler was able to interpret the observations and deduced three laws, one of which had a great

impact on later discoveries. He deduced that, for a circular orbit of a planet around the Sun, if T is

the period of rotation and r is the radius of the orbit, then

T2 r

3 .

As a result of Kepler's work Newton formulated the law of gravitation.

(a) (i) State an equation representing Newton's law of gravitation, explaining the symbols

used.

[2]

(ii) By relating the gravitational force on a planet to the centripetal acceleration it causes, show that, for a circular orbit,

T2 =

4π2r

3

GM .

[2]


11 Page

(b) The planet Jupiter has a number of moons. Data for some of these are given in Fig. 7.1.

moon

period

T/days

Mean distance from centre

of Jupiter r/109m

log10(T/days)

log10(r/m)

Sinope 758 23.7 2.88 10.37

Leda 239 11.1

Callisto 16.7 1.88

Lo 1.77 0.422

Metis 0.295 0.128 -0.530 8.11

Fig. 7.1

(i) Complete Fig. 7.1 by calculating values for log10(T/days) and log10(r/m). [1]

(ii) On the axes of Fig. 7.2, plot a graph of log10(T/days) against log10(r/m). [2]

(c) (i) Determine the gradient of the graph in Fig. 7.2.

gradient = ……………….. [1]

(ii) Hence discuss whether the data in Fig. 7.1 support the relation given in (a)(ii).

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

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

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

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

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

…………………………………………………………………………..........[3]


12 Page

Fig. 7.2

(d) Observation shows that the moon Ganymede orbits Jupiter with a period of 7.16 days. Use

the graph of Fig. 7.2 to estimate the orbital radius of Ganymede.

radius = ………….. m [2]

log10 (T / days)


13 Page

(e) Suggest whether the graph of Fig. 7.2 could be used to check data on the orbital radii and

periods of the moons of another planet (e.g. Saturn).

…………………………………………………………………………………...

…………………………………………………………………………………...

…………………………………………………………………………………...

…………………………………………………………………………………...

………………………………………………………………………………. [2]

2010 TJC H2 P3 Q5c, 5d

6 (c) Write down an equation to represent Newton’s Law of Gravitation, stating clearly the

symbols used.

[2]

(d) Data for a certain planet orbiting about a star are given below:

Mass of planet = 1.20 x 1024

kg

Diameter of planet = 7.50 x 106 m

Diameter of star = 7.00 x 108 m

Orbital period of planet = 3.45 x 107 s

Distance from centre

of planet to centre of star

= 2.00 x 1011

m

(i) Calculate the mass of the star.


14 Page

mass of star =

kg

[3]

(ii) In the absence of other celestial bodies, the only force acting on the star and the

planet is the gravitational force of attraction they exert on each other. Explain

why the planet does not accelerate and crash into the star.

[2]

(iii) Use the data given to calculate the escape velocity of a mass on the planet. Ignore

the gravitational effects of the star on the mass.

escape velocity = m s-1

[3]

(iv) An atmosphere is formed when gases such as nitrogen is allowed to orbit around

the planet. Given that the average speed of a molecule of nitrogen at the surface

of the planet is 3.9 x 104 m s

-1, explain whether the planet has an atmosphere.

[1]


15 Page

2010 YJC H2 P2 Q1

7 (a) State Newton’s law of gravitation. [2]

..…………………………………………………………………………………

..…………………………………………………………………………………

..…………………………………………………………………………………

(b) A source reported that Singapore plans to launch a satellite that will orbit around the Earth at

2.5 103

m above its surface in the year 2020. Take the radius of Earth to be 6.38 106 m

and mass of Earth to be 5.97 1024

kg.

(i) Calculate the linear velocity of the satellite when in orbit. [2]

Linear velocity = …………….. m s−1

(ii) Deduce whether the satellite is geostationary. [2]

(iii) If the satellite were to orbit above the equator, state the direction of launch, in order to

minimize energy required. [1]

………………………………………………………………………………


16 Page

2010 SRJC H2 P3 Q6

8(a) (i) The gravitational force is significant only when we deal with celestial objects like stars and planets

but not with atoms or molecules. Explain the rationale for this statement. [2]

(ii) It is often said that astronauts experience weightlessness only because they are beyond the pull of the

Earth’s gravity. Comment on the validity of this statement. [2]

(iii) Rockets are usually launched at locations near the Equator in an easterly direction. Explain whether

there is any advantage in launching a rocket to the east versus launching to the west.

[2]

(b) An Earth satellite in a circular orbit has a period of 12 hours about the Earth’s centre. The radius of the

Earth is 6.40 x 103 km.

Calculate

(i) the mass of the Earth given that the acceleration of free fall at its surface is 9.81 m s-2.

mass = …………………… kg [2]


17 Page

(ii) the height of the satellite above the Earth’s surface.

height = …………………… m [3]

(iii) the orbital speed of the satellite.

speed = …………………… m s-1 [2]

(c) (i) The satellite is directly above an observer located at the Equator at certain instant of time. The

satellite moves in the same direction of rotation as the Earth. Describe the motion of the satellite relative to

the observer over the next 24 hours. Consider two 12 hour periods.

[2]

(ii) Determine the orbital period for the satellite to be geostationary.

period = ……………………. hr [1]

(iii) List one advantage and one disadvantage to the observer if the satellite was geostationary. [2]

advantage:

disadvantage:


18 Page

(d) Gravitational and electric fields have analogous characteristics. List one similarity and one difference

between these two fields.

[1]

2010 TPJC H2 P3 Q6

9 (a) The gravitational field strength of the Earth at a point P that is 2100 km above its surface is 5.56 N kg-1

.

(i) Show that the acceleration of free fall at P is 5.56 m s-2

.[2]

(ii) Determine the gravitational force exerted on a 5.0 kg mass at point P. [2]

(iii) Show that N kg-1

is equivalent to m s-2

in base units. [1]

(b) (i) Define gravitational potential at a point. [1]


19 Page

(ii) Given that the Earth has a mass of 5.98 x 1024

kg and a radius of 6.37 x 106

m, determine the

gravitational potential at

1. point P, which is at a height of 2100 km above the surface.

2. point Q, which is at a height of 4200 km above the surface. [3]

(iii) Hence determine the work done in bringing a 5.0 kg mass from point P to point Q without changing its

kinetic energy. [2]

(c) Explain whether the answer to (b)(iii) can be calculated by using the equation

Work done = force x displacement,

where the force is the value calculated in (a)(ii) and the displacement is 2100 km. [2]

(d) A weather satellite is sent up to a polar orbit that contains point P.

(i) Determine the period of the satellite.[3]


20 Page

(ii) Determine the linear velocity of the satellite. [2]

(iii) State one advantage of having the weather satellite in this polar orbit as compared to the geostationary

satellite which has an orbital radius of 42 000 km. [1]

(iv) Explain why despite being attracted by Earth’s gravitational force, the orbiting weather satellite will not

fall down to the Earth. [1]

2010 IJC H2 P2 Q3

10 Fig. 3.1 shows a binary star system where two identical stars each of mass 4.01030

kg are moving with

a constant speed v in a circular orbit of radius 1.01011

m about their common centre of mass.


21 Page

Fig. 3.1

You may assume that each star to be a uniform sphere with its mass concentrated at the centre of the

sphere.

(a) (i) On Fig. 3.1, label with the letter ‘X’ a point where the gravitational field strength is zero.

[1]

(ii) Explain why you have chosen the point in (i).

………………………………………………………………………………………………

..………………………………..………………………………………………………. [1]

(iii) Calculate the gravitational potential at point X.

gravitational potential = ………………………… J kg-1

[2]

(b) For each star in the system, calculate

(i) the net force,

net force = ………………………… N [2]

1.01011 m

star

star

v

v


22 Page

(ii) the linear speed v.

linear speed = ………………………… m s-1

[2]

2010 JJC H2 P3 Q1

11. Fig. 1 below illustrates a satellite of mass 425 kg placed at a point X, a distance of 1.60 x 109

m from the centre of the Earth, in order to observe the Sun continuously.

Fig. 1

(a) Using the data given, determine the magnitude and direction of the resultant force

acting on the satellite. [3]

Mass of Sun = 1.99 x 1030 kg Mass of Earth = 5.98 x 1024 kg Pull of the Earth on the satellite = 0.0662 N

Earth Sun

X

1.50 x 1011

m

1.60 x 109 m


23 Page

(b) (i) Given that the satellite is in a circular orbit around the Sun, determine its

acceleration. [1]

(ii) Hence or otherwise, calculate its angular velocity. [2]

(c) Write out two disadvantages of having a satellite orbiting around the Sun. [2]

2010 MJC H2 P3 Q2

12 (a) It is often assumed that air resistance acting on a moving object will result in the

object slowing down. Air resistance can however indirectly make an object speed

up. Consider a 1000 kg satellite orbiting at 280 km above the Earth’s surface. A

small force of air resistance makes the satellite descend into a circular orbit with an

altitude of 100 km.

[Radius of Earth = 6.37 x 106 m, mass of Earth = 5.98 x 10

24 kg]

(i) By calculating the speed of the satellite at both orbits, show that the satellite

is indeed travelling faster at the lower orbit. [3]


24 Page

(ii) Show that the total mechanical energy of the satellite, E can be expressed as:

E s

o2

GM mE

R

where ME is the mass of earth, ms is the mass of satellite and, Ro is the radius

of orbit. [2]

(iii) Explain the significance of the negative sign in the expression for the total

mechanical energy of the satellite.

………………………………………………………………………………

…........

………………………………………………………………………………

…........

…………………………………………………………………………

….....

[1]

(iv) Hence, calculate the change in mechanical energy due to air resistance.


25 Page

change in mechanical energy ……………….. J [2]

(b) Black holes are formed when massive stars collapse towards a singularity i.e. a

point mass. There exist a boundary, known as the event horizon, surrounding a

black hole where a even body travelling at the speed of light (if it is possible) can

barely escape.

Consider the gravitational potential energy of the body at the event horizon, deduce

an expression for the radius of the event horizon, event horizonR in terms of the mass of

the black hole, M and speed of light c.

event horizonR ……………….. [2]

2010 AJC H2 P2 Q2

13 (a)(i) On Fig. 2.1, draw lines to represent the gravitational field outside an isolated uniform sphere.

(ii) A second sphere has the same mass but a smaller radius. Suggest what difference, if any, there is

between the patterns of field lines for the two spheres.

(b) The Earth may be considered to be a uniform sphere of radius 6380 km with its mass of 5.98 × 1024

kg concentrated at its centre, as illustrated in Fig. 2.2

Fig. 2.1


26 Page

Fig. 2.2

A mass of 10.0 kg on the Equator rotates about the axis of the Earth with a period of 1.00 day.

Calculate,

(i) the gravitational force FG of attraction between the mass and the Earth,

(ii) the centripetal force FC on the 10.0 kg mass,

(iii) the difference in magnitude of the forces

(c) By reference to your answers in (b), suggest, with a reason, a value for the acceleration of free fall at the

Equator.

END

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