Question 1

1 mark

A light spring with a spring constant of

100\,\text{N m}^{-1}

is stretched from an extension of

10\,\text{cm}

to an extension of

20\,\text{cm}

. The spring remains within its limit of proportionality throughout the process. What is the additional elastic potential energy stored in the spring during this extension?

A. $0.5\,\text{J}$
B. $1.0\,\text{J}$
C. $1.5\,\text{J}$
D. $2.0\,\text{J}$
E. $3.0\,\text{J}$

Answer: C

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Question 2

1 mark

A block

X

of mass

4.0\,\text{kg}

is placed on a smooth, horizontal table. It is connected by a light, inextensible string that passes over a frictionless pulley at the edge of the table to a hanging weight

Y

of mass

1.0\,\text{kg}

. The system is released from rest.

What is the magnitude of the tension in the string while the masses are in motion?
(The gravitational field strength

g

is

10\,\text{N kg}^{-1}

.)

A.2.0 N
B.4.0 N
C.8.0 N
D.10 N
E.12 N

Answer: C

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Question 3

1 mark

A car of mass

1200\,\text{kg}

is towing a trailer of mass

800\,\text{kg}

along a straight, horizontal road. The car and trailer accelerate together at a constant rate of

1.5\,\text{m s}^{-2}

. During this acceleration, the trailer experiences a constant resistive force of

300\,\text{N}

.

What is the magnitude of the force exerted by the trailer on the car?

A.300 N
B.900 N
C.1200 N
D.1500 N
E.3000 N

Answer: D

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Question 4

1 mark

A weather sensor of mass

12\,\text{kg}

is falling vertically through the air. After some time, a small parachute is deployed to slow its descent. At a specific instant after the parachute has opened, the air resistance acting on the system is

300\,\text{N}

. What is the magnitude and direction of the acceleration of the sensor at this instant?
(The gravitational field strength

g

is

10\,\text{N kg}^{-1}

.)

A. $10\,\text{m s}^{-2}$ downwards
B. $15\,\text{m s}^{-2}$ downwards
C. $15\,\text{m s}^{-2}$ upwards
D. $25\,\text{m s}^{-2}$ upwards
E. $35\,\text{m s}^{-2}$ upwards

Answer: C

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Question 5

1 mark

Two spheres,

P

and

Q

, have identical dimensions and surface textures but are made of different materials. Sphere

P

has a mass of

3.0\,\text{kg}

and sphere

Q

has a mass of

5.0\,\text{kg}

. Both spheres are dropped from a high altitude. Sphere

P

is observed to reach a terminal velocity of

40\,\text{m s}^{-1}

. Assuming that air resistance depends only on the speed and the dimensions of the object, what is the magnitude of the acceleration of sphere

Q

at the instant its speed is

40\,\text{m s}^{-1}

?
(The gravitational field strength

g

is

10\,\text{N kg}^{-1}

.)

A. $0\,\text{m s}^{-2}$
B. $4.0\,\text{m s}^{-2}$
C. $6.0\,\text{m s}^{-2}$
D. $10\,\text{m s}^{-2}$
E. $16\,\text{m s}^{-2}$

Answer: B

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Question 6

1 mark

An electric car of mass

1200\text{ kg}

is accelerated from rest to a speed of

20\text{ m s}^{-1}

along a straight, horizontal road. The car's motor provides a constant input power of

60\text{ kW}

and operates at an overall efficiency of

80\%

. Assuming air resistance is negligible, how long does the car take to reach this speed?

A.3.2 s
B.4.0 s
C.5.0 s
D.6.25 s
E.10.0 s

Answer: C

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Question 7

1 mark

A block of mass

5.0\text{ kg}

is pulled from rest up a rough slope by a constant force of

50\text{ N}

acting parallel to the slope. The slope has a length of

10\text{ m}

and reaches a vertical height of

6.0\text{ m}

. When the block reaches the top of the slope, it has a speed of

4.0\text{ m s}^{-1}

. Using

g = 10\text{ m s}^{-2}

, what is the work done against friction during this process?

A.40 J
B.160 J
C.200 J
D.300 J
E.340 J

Answer: B

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Question 8

1 mark

Two metal rods,

X

and

Y

, have the same length

L

. Rod

X

has a diameter

d

and is made of a metal with thermal conductivity

k

. Rod

Y

has a diameter

2d

and is made of a metal with thermal conductivity

0.5k

. If the same temperature difference

\Delta T

is maintained between the ends of each rod, what is the ratio of the rate of thermal energy transfer through rod

Y

to the rate of thermal energy transfer through rod

X

?

A. $0.25$
B. $0.5$
C. $1.0$
D. $2.0$
E. $4.0$

Answer: D

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Question 9

1 mark

Two identical solid cubes,

X

and

Y

, are placed in a room where the air and walls are maintained at a constant temperature of

25^\circ\text{C}

. Cube

X

is at an initial temperature of

15^\circ\text{C}

and cube

Y

is at an initial temperature of

35^\circ\text{C}

. Both cubes have the same dull black surface finish. Which of the following statements correctly compares the initial rates of emission and absorption of infrared radiation for the two cubes?

A.Cube $Y$ emits radiation at a higher rate than cube $X$ , and cube $X$ absorbs radiation at a higher rate than cube $Y$ .
B.Cube $X$ emits radiation at a higher rate than cube $Y$ , and cube $Y$ absorbs radiation at a higher rate than cube $X$ .
C.Cube $Y$ emits radiation at a higher rate than cube $X$ , and both cubes absorb radiation at the same rate.
D.Both cubes emit radiation at the same rate, but cube $X$ absorbs radiation at a higher rate than cube $Y$ .
E.Both cubes emit and absorb radiation at the same rate because they have the same surface area and color.

Answer: C

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Question 10

1 mark

Two metal spheres,

M

and

N

, are placed in a vacuum. Sphere

M

has a radius

R

and a dull black surface. Sphere

N

has a radius

3R

and a shiny polished surface. At any given temperature, the rate of infrared radiation emission per unit surface area for the dull black surface is

12

times that of the shiny polished surface. Both spheres are initially at the same temperature

T

. Let

P_M

be the initial power emitted by sphere

M

and

P_N

be the initial power emitted by sphere

N

. What is the ratio

\frac{P_M}{P_N}

?

A. $\frac{4}{3}$
B. $\frac{3}{4}$
C. $4$
D. $9$
E. $12$

Answer: A

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Question 11

1 mark

Two metal blocks, X and Y, are heated using identical electric heaters. Block X has mass

m

and specific heat capacity

c

. Block Y has mass

3m

and specific heat capacity

2c

. The heater for block X is switched on for a time

t

, and the heater for block Y is switched on for a time

4t

. Assuming

100\%

efficiency for both heaters and no heat loss to the surroundings, what is the ratio of the temperature change of block Y to the temperature change of block X,

\frac{\Delta T_Y}{\Delta T_X}

?

A.1/6
B.2/3
C.3/2
D.6
E.24

Answer: B

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Question 12

1 mark

A substance in the solid state has a density of

\rho_{\text{s}} = 1600\,\text{kg m}^{-3}

. When the substance sublimates to form a gas, its density decreases to

\rho_{\text{g}} = 0.20\,\text{kg m}^{-3}

. In the solid, particles are modeled as spheres of diameter

D

packed tightly in a simple cubic arrangement such that each particle occupies a cubic volume

V_{\text{s}} = D^3

. In the gas, each particle is modeled as occupying an average cubic volume

V_{\text{g}} = d^3

, where

d

is the average distance between the centers of adjacent particles. What is the ratio of the average distance between the surfaces of adjacent particles in the gas to the particle diameter

D

?

A.19
B.20
C.88
D.400
E.7999

Answer: A

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Question 13

1 mark

A substance with molar mass

M = 0.024\,\text{kg mol}^{-1}

exists as a liquid with density

\rho = 1200\,\text{kg m}^{-3}

. It evaporates to form an ideal gas at a temperature

T = 300\,\text{K}

and a pressure

P = 1.2 \times 10^5\,\text{Pa}

. In both states, we use a simple model where each particle (molecule) occupies a cubic volume

V_{\text{p}} = d^3

, where

d

is the average distance between the centers of adjacent particles. Using

R = 8.0\,\text{J mol}^{-1}\,\text{K}^{-1}

, what is the ratio of the average distance between particles in the gas state to that in the liquid state,

\frac{d_{\text{g}}}{d_{\text{l}}}

?

A.4.6
B.10
C.31.6
D.100
E.1000

Answer: B

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Question 14

1 mark

A long vertical tube, closed at one end, contains a

2.0\text{ m}

column of oil that traps an

80\text{ cm}

column of an ideal gas at the closed end. Initially, the tube is oriented with its open end facing upwards. The atmospheric pressure is equivalent to the pressure exerted by a

10.0\text{ m}

column of the same oil. The tube is then slowly inverted until its open end faces downwards. Assuming the temperature of the gas remains constant and no oil is lost from the tube, what is the distance moved by the oil column relative to the tube?

A.16 cm
B.20 cm
C.40 cm
D.80 cm
E.120 cm

Answer: C

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Question 15

1 mark

A

100\,\text{g}

block of ice is initially at a temperature of

-20\,^\circ\text{C}

. A heater provides energy to the ice at a constant rate of

200\,\text{W}

. Assuming no energy is lost to the surroundings, how much time does it take for the block to reach a state where exactly

50\,\text{g}

of the ice has melted into water at

0\,^\circ\text{C}

?

(Take the specific heat capacity of ice to be

c_{ice} = 2.1\,\text{Jg}^{-1}\,^\circ\text{C}^{-1}

and the specific latent heat of fusion of ice to be

L_f = 334\,\text{Jg}^{-1}

.)

A.21.0 s
B.83.5 s
C.104.5 s
D.125.5 s
E.188.0 s

Answer: C

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Question 16

1 mark

A siren on a vehicle emits sound at a constant frequency

f_s

. The vehicle moves at a constant speed

v

along a straight path toward a stationary observer. The observer measures the frequency of the sound to be

f_1 = \frac{5}{4}f_s

. After the vehicle passes the observer and continues to move at the same speed

v

in the opposite direction, the observer measures a new frequency

f_2

. If the speed of sound in air is

c

, which of the following is the correct expression for

f_2

?

A. $\frac{3}{4} f_s$
B. $\frac{4}{5} f_s$
C. $\frac{5}{6} f_s$
D. $\frac{6}{7} f_s$
E. $\frac{2}{3} f_s$

Answer: C

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Question 17

1 mark

A ray of monochromatic light travels through a transparent medium with refractive index

n

and speed

v_{\text{m}}

. The ray strikes a flat boundary with air at an angle of incidence

\theta

. Some light is reflected back into the medium and some is refracted into the air. The reflected ray and the refracted ray are found to be perpendicular to each other. If the speed of light in air is

v_{\text{a}}

, which of the following expressions gives the speed of light in the medium,

v_{\text{m}}

?

A. $v_{\text{a}} \sin \theta$
B. $v_{\text{a}} \cos \theta$
C. $v_{\text{a}} \tan \theta$
D. $v_{\text{a}} / \tan \theta$
E. $v_{\text{a}} / \sin \theta$

Answer: C

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Question 18

1 mark

A medical ultrasound probe is placed against a patient's skin to examine two adjacent layers of tissue,

X

and

Y

. Both layers have the same thickness

L

. The speed of sound is

v_X

in tissue

X

and

v_Y

in tissue

Y

. A pulse is emitted at time

t = 0

. The first echo (Echo 1, from the interface between

X

and

Y

) is received at time

t_1

. The second echo (Echo 2, from the far boundary of

Y

) is received at time

t_2

. Assuming the probe is adjacent to the surface of layer

X

, which of the following expressions gives the ratio

\frac{t_2}{t_1}

?

A. $\frac{v_X + v_Y}{v_X}$
B. $\frac{v_X + v_Y}{v_Y}$
C. $\frac{v_X}{v_Y}$
D. $\frac{v_Y}{v_X}$
E. $\frac{v_X + v_Y}{2v_Y}$

Answer: B

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Question 19

1 mark

Two small speakers are placed

25.0\text{ cm}

apart and are connected to a signal generator that produces sound waves in phase. A microphone is positioned

60.0\text{ cm}

from the first speaker such that the line connecting the microphone to the first speaker is perpendicular to the line connecting the two speakers. The signal generator's frequency

f

is increased from

1.0\text{ kHz}

to

25.0\text{ kHz}

. The speed of sound is

340\text{ m s}^{-1}

. How many of the frequencies in this range that produce a local maximum in intensity at the microphone are audible to humans? (Assume the range of human hearing is

20\text{ Hz}

to

20\text{ kHz}

).

A.1
B.2
C.3
D.4
E.5

Answer: B

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Question 20

1 mark

Two electromagnetic waves,

X

and

Y

, travel through a vacuum. Wave

X

has a wavelength

\lambda_X = 6.0 \times 10^{-5}\,\text{m}

. Wave

Y

has a frequency

f_Y

such that the ratio of the frequency of

Y

to the frequency of

X

is:

\frac{f_Y}{f_X} = 2.0 \times 10^5

Which row in the table correctly identifies the nature of wave

Y

, its wavelength in a vacuum, and a common hazard or application associated with it?
(The speed of light in a vacuum is

c = 3.0 \times 10^8\,\text{m}\,\text{s}^{-1}

)

A.nature: X-ray; wavelength: $3.0 \times 10^{-10}\,\text{m}$ ; application: medical imaging of bones
B.nature: Gamma ray; wavelength: $3.0 \times 10^{-15}\,\text{m}$ ; application: sterilising medical equipment
C.nature: Ultraviolet; wavelength: $3.0 \times 10^{-10}\,\text{m}$ ; hazard: causes skin cancer
D.nature: X-ray; wavelength: $3.0 \times 10^{-5}\,\text{m}$ ; application: satellite communications
E.nature: Radio wave; wavelength: $1.2 \times 10^1\,\text{m}$ ; application: local radio broadcasting

Answer: A

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Question 21

1 mark

Three components of the electromagnetic spectrum,

P

,

Q

, and

R

, are characterized by the following properties in a vacuum:
-

P

has a wavelength of

2.5 \times 10^{-8}\,\text{m}

-

Q

has a frequency of

4.0 \times 10^{13}\,\text{Hz}

-

R

has a period of

5.0 \times 10^{-20}\,\text{s}

(The speed of light in a vacuum is

c = 3.0 \times 10^8\,\text{m}\,\text{s}^{-1}

.)
Which row in the table correctly identifies the nature of

P, Q,

and

R

and lists them in order of **increasing** wavelength?

A.P: Ultraviolet; Q: Infrared; R: Gamma ray; order: R, P, Q
B.P: Ultraviolet; Q: Microwave; R: X-ray; order: R, P, Q
C.P: Visible light; Q: Infrared; R: Gamma ray; order: P, R, Q
D.P: X-ray; Q: Infrared; R: Gamma ray; order: R, P, Q
E.P: Ultraviolet; Q: Infrared; R: Gamma ray; order: Q, P, R

Answer: A

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Question 22

1 mark

A neutral atom of an isotope of element

X

has a mass number of

65

and contains

35

neutrons. This atom loses two electrons to form an ion

X^{2+}

.

What is the atomic number of

X

and the number of electrons in the ion

X^{2+}

?

A.atomic number: $30$ ; number of electrons: $28$
B.atomic number: $30$ ; number of electrons: $32$
C.atomic number: $35$ ; number of electrons: $33$
D.atomic number: $35$ ; number of electrons: $37$
E.atomic number: $65$ ; number of electrons: $63$

Answer: A

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Question 23

1 mark

Consider the following three nuclides:

^{14}_{6}\text{C}, \quad ^{13}_{6}\text{C}, \quad ^{14}_{7}\text{N}

Which one of the following statements is correct?

A. $^{14}_{6}\text{C}$ and $^{13}_{6}\text{C}$ are isotopes, and $^{13}_{6}\text{C}$ and $^{14}_{7}\text{N}$ have the same number of neutrons.
B. $^{14}_{6}\text{C}$ and $^{14}_{7}\text{N}$ are isotopes, and $^{14}_{6}\text{C}$ and $^{13}_{6}\text{C}$ have the same mass number.
C. $^{14}_{6}\text{C}$ and $^{13}_{6}\text{C}$ have the same number of neutrons, and $^{13}_{6}\text{C}$ and $^{14}_{7}\text{N}$ are isotopes.
D. $^{14}_{6}\text{C}$ and $^{14}_{7}\text{N}$ have the same number of protons, and $^{13}_{6}\text{C}$ and $^{14}_{7}\text{N}$ have the same mass number.
E. $^{14}_{6}\text{C}$ and $^{13}_{6}\text{C}$ have different atomic numbers, and $^{14}_{6}\text{C}$ and $^{14}_{7}\text{N}$ have the same number of neutrons.

Answer: A

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Question 24

1 mark

A nucleus of thorium-232 (

^{232}_{90}\text{Th}

) decays through a series of emissions to become a stable nucleus of lead-208 (

^{208}_{82}\text{Pb}

). The emissions consist only of alpha (

\alpha

) particles and beta-minus (

\beta^-

) particles. What is the total decrease in the number of neutrons in the nucleus during this process, and how many of these lost neutrons are converted into protons?

A.total decrease in neutrons: 12; neutrons converted to protons: 4
B.total decrease in neutrons: 16; neutrons converted to protons: 4
C.total decrease in neutrons: 16; neutrons converted to protons: 8
D.total decrease in neutrons: 24; neutrons converted to protons: 4
E.total decrease in neutrons: 24; neutrons converted to protons: 8

Answer: B

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Question 25

1 mark

Three radioactive sources emit different types of radiation labelled

X

,

Y

, and

Z

:

- Radiation

X

is stopped by a thin sheet of paper.
- Radiation

Y

is stopped by a few millimetres of aluminium.
- Radiation

Z

can only be significantly attenuated by several centimetres of lead.

Which statement about the relative ionising powers and the deflection of these radiations in a uniform magnetic field is correct?

A. $X$ is the most ionising and $Z$ is not deflected.
B. $X$ is the least ionising and $Z$ is not deflected.
C. $Y$ is the most ionising and $X$ is not deflected.
D. $Z$ is the most ionising and $Y$ is not deflected.
E. $Z$ is the least ionising and $X$ is not deflected.

Answer: A

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Question 26

1 mark

A student uses a Geiger-Müller tube to measure the count rate of a radioactive isotope in a laboratory. The background count rate is constant at

20\,\text{counts per minute}

.

At time

t = 0

, the measured total count rate is

180\,\text{counts per minute}

.
At time

t = 30\,\text{minutes}

, the measured total count rate is

40\,\text{counts per minute}

.

What is the half-life of the radioactive isotope?

A. $6\,\text{minutes}$
B. $7.5\,\text{minutes}$
C. $10\,\text{minutes}$
D. $15\,\text{minutes}$
E. $20\,\text{minutes}$

Answer: C

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Question 27

1 mark

A radioactive isotope P decays into a stable isotope Q with a half-life of

20\text{ days}

. Another radioactive isotope R decays into a stable isotope S with a half-life of

40\text{ days}

. A sample is prepared containing equal numbers of atoms of P and R, and no atoms of Q or S. What is the ratio of the number of atoms of Q to the number of atoms of S in the sample after

80\text{ days}

have passed?

A. $1:4$
B. $4:5$
C. $5:4$
D. $15:4$
E. $15:16$

Answer: C

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Question 28

1 mark

A circuit consists of an ideal

12\text{ V}

battery connected in series with two units,

X

and

Y

. Unit

X

consists of a fixed

100\,\Omega

resistor and an NTC thermistor connected in parallel. Unit

Y

consists of a fixed

200\,\Omega

resistor and a light-dependent resistor (LDR) connected in parallel. At a specific temperature and light level, the resistance of the thermistor is

100\,\Omega

and the resistance of the LDR is

200\,\Omega

. What is the power dissipated in the

200\,\Omega

fixed resistor in unit

Y

?

A. $0.08\text{ W}$
B. $0.18\text{ W}$
C. $0.32\text{ W}$
D. $0.64\text{ W}$
E. $0.72\text{ W}$

Answer: C

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Question 29

1 mark

A student has two initially unmagnetized rods of identical appearance. Rod

X

is made of soft iron and rod

Y

is made of hard steel. Both rods are placed in contact with the North pole of a strong permanent bar magnet for several minutes. The permanent magnet is then removed and placed far away. The student then tests the rods by bringing each one close to a sensitive magnetic compass and then into a pile of small iron filings. Which of the following observations is most likely?

A.Both rod $X$ and rod $Y$ will significantly deflect the compass needle and pick up many iron filings.
B.Neither rod $X$ nor rod $Y$ will deflect the compass needle or pick up any iron filings.
C.Rod $X$ will significantly deflect the compass needle, but rod $Y$ will show almost no magnetic effect.
D.Rod $Y$ will significantly deflect the compass needle, but rod $X$ will show almost no magnetic effect.
E.Both rods will repel the North pole of the compass needle regardless of which end of the rod is used.

Answer: D

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Question 30

1 mark

A bar magnet is placed under a sheet of paper and iron filings are used to map the magnetic field. The filings show a pattern where the field lines emerge from end

P

of the magnet and enter end

Q

. A second, identical bar magnet is then brought towards the first one so that its South pole faces end

Q

. Which of the following correctly identifies the pole at

Q

and the nature of the force between end

Q

and the second magnet?

A.End $Q$ is a North pole, and it attracts the South pole of the second magnet.
B.End $Q$ is a North pole, and it repels the South pole of the second magnet.
C.End $Q$ is a South pole, and it attracts the South pole of the second magnet.
D.End $Q$ is a South pole, and it repels the South pole of the second magnet.
E.End $Q$ is a South pole, and there is no magnetic force between them.

Answer: D

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ESAT Mock Physics Esat-physics-bank-3

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24

Question 25

Question 26

Question 27

Question 28

Question 29

Question 30