Question 1

1 mark

A power station generates

2.0\,\text{MW}

of electrical power which is transmitted through a long-distance cable with a total resistance of

10\,\Omega

. The power is transmitted at a voltage of

50\,\text{kV}

. What is the rate at which electrical energy is dissipated as heat in the cable?

A. $0.40\,\text{kW}$
B. $1.6\,\text{kW}$
C. $16\,\text{kW}$
D. $160\,\text{kW}$
E. $400\,\text{kW}$

Answer: C

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Question 2

1 mark

A cyclist starts from rest and accelerates at a constant rate of

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

for

6.0\,\text{s}

. The cyclist then travels at a constant velocity for

10.0\,\text{s}

. Finally, the cyclist decelerates uniformly to a stop in

4.0\,\text{s}

. What is the average speed of the cyclist for the entire

20.0\,\text{s}

journey?

A.6.0\, $\text{m s}$ ^{-1}
B.8.0\, $\text{m s}$ ^{-1}
C.9.0\, $\text{m s}$ ^{-1}
D.10.2\, $\text{m s}$ ^{-1}
E.12.0\, $\text{m s}$ ^{-1}

Answer: C

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Question 3

1 mark

A research probe of mass

200\text{ kg}

is suspended by a light vertical cable from a weather balloon. The balloon and the probe are both moving vertically upwards. At a certain instant, the probe is accelerating upwards at

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

and experiences a downward air resistance (drag) force of

400\text{ N}

.

What is the tension in the cable at this instant?
(gravitational field strength

g = 10\text{ N kg}^{-1}

)

A.1900 N
B.2100 N
C.2300 N
D.2400 N
E.2700 N

Answer: E

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Question 4

1 mark

Two blocks, P and Q, are stacked inside a crate. Block P, with a mass of

3.0\text{ kg}

, is placed on top of block Q, which has a mass of

5.0\text{ kg}

. The crate has a mass of

2.0\text{ kg}

and is being pulled vertically upwards by a crane. At a specific moment, the crate and its contents are accelerating upwards at

2.0\text{ m s}^{-2}

.

What is the magnitude of the normal contact force exerted by block Q on the floor of the crate?
(gravitational field strength

g = 10\text{ N kg}^{-1}

)

A.60 N
B.64 N
C.80 N
D.96 N
E.120 N

Answer: D

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Question 5

1 mark

A light platform is supported by two vertical springs,

X

and

Y

, connected in parallel to a fixed base. Spring

X

has a spring constant

k

, and spring

Y

has a spring constant

3k

. A block of mass

m

is placed on the platform and descends slowly until it reaches an equilibrium position, compressing both springs. The total elastic potential energy stored in the springs at this point is

U

.

The block is then removed, and spring

Y

is replaced with a different spring

Z

of spring constant

k_Z

. When the same block of mass

m

is placed on the platform and reaches equilibrium, the total elastic potential energy stored in the springs is

2U

.

Assuming all springs remain within their limit of proportionality, what is the value of

k_Z

?

A. $k$
B. $2k$
C. $3k$
D. $7k$
E. $8k$

Answer: A

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Question 6

1 mark

Three blocks

P

,

Q

, and

R

with masses

2.0\,\text{kg}

,

3.0\,\text{kg}

, and

5.0\,\text{kg}

respectively are connected by two light inextensible strings and rest on a smooth horizontal surface. String 1 connects blocks

P

and

Q

. String 2 connects blocks

Q

and

R

. A constant horizontal force of

30\,\text{N}

is applied to block

R

, pulling the system in a straight line away from blocks

Q

and

P

.

What is the tension in String 1?

A. $6.0\,\text{N}$
B. $9.0\,\text{N}$
C. $15\,\text{N}$
D. $21\,\text{N}$
E. $30\,\text{N}$

Answer: A

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Question 7

1 mark

A storage crate has a mass of

12\,\text{kg}

on Earth. It is transported to a research station on a moon where the gravitational field strength is

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

. A winch pulls the crate vertically upwards with a constant force of

60\,\text{N}

. What is the magnitude of the crate’s acceleration on this moon?
(The gravitational field strength on Earth is

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

.)

A. $2.0\,\text{m s}^{-2}$
B. $3.0\,\text{m s}^{-2}$
C. $5.0\,\text{m s}^{-2}$
D. $7.0\,\text{m s}^{-2}$
E. $10\,\text{m s}^{-2}$

Answer: B

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Question 8

1 mark

A skydiver of mass

80\,\text{kg}

is falling vertically. At a specific moment after the parachute is deployed, the upward air resistance acting on the skydiver and equipment is

1200\,\text{N}

. What is the magnitude and direction of the skydiver's acceleration at this moment?
(The gravitational field strength

g

is

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

.)

A. $5.0\,\text{m s}^{-2}$ downwards
B. $5.0\,\text{m s}^{-2}$ upwards
C. $10\,\text{m s}^{-2}$ downwards
D. $15\,\text{m s}^{-2}$ upwards
E. $25\,\text{m s}^{-2}$ upwards

Answer: B

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Question 9

1 mark

An object of mass

8.0\,\text{kg}

is travelling at

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

in a straight line on a smooth horizontal surface when it explodes into two fragments, P and Q, of mass

2.0\,\text{kg}

and

6.0\,\text{kg}

respectively. The explosion increases the total kinetic energy of the system by

192\,\text{J}

. Immediately after the explosion, the smaller fragment, P, is moving in the original direction of motion of the object. What is the velocity of fragment Q immediately after the explosion?

0. $6.0\,\text{m s}^{-1}$ in the original direction of motion
A. $2.0\,\text{m s}^{-1}$ in the opposite direction to the original motion
B. $2.0\,\text{m s}^{-1}$ in the original direction of motion
C. $6.0\,\text{m s}^{-1}$ in the opposite direction to the original motion
E. $14\,\text{m s}^{-1}$ in the original direction of motion

Answer: A

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Question 10

1 mark

A horizontal jet of water is delivered by a pump at a constant rate of

5.0\,\text{litres per second}

through a hose with a cross-sectional area of

2.0 \times 10^{-4}\,\text{m}^2

. The water strikes a vertical wall normally (at

90^\circ

) and rebounds directly backwards with a speed of

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

. What is the magnitude of the average force exerted on the wall by the water? (Density of water =

1000\,\text{kg m}^{-3}

;

1.0\,\text{litre} = 1.0 \times 10^{-3}\,\text{m}^3

.)

A. $25\,\text{N}$
B. $100\,\text{N}$
C. $125\,\text{N}$
D. $150\,\text{N}$
E. $250\,\text{N}$

Answer: D

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Question 11

1 mark

A motor-driven crane lifts a

20\text{ kg}

crate vertically at a constant speed. The crate is raised through a height of

12\text{ m}

in a time of

20\text{ s}

. The average electrical power supplied to the crane's motor is

200\text{ W}

. Taking the gravitational field strength

g = 10\text{ N kg}^{-1}

, what is the percentage efficiency of the crane system?

A.12%
B.40%
C.60%
D.80%
E.120%

Answer: C

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Question 12

1 mark

A rectangular loop of tubing, oriented vertically as shown, is completely filled with an oil whose density decreases as its temperature increases. A small heating element is installed at the bottom of the right-hand vertical section. Simultaneously, a cooling jacket is applied to the top of the left-hand vertical section. Once a steady state is established, which of the following describes the resulting circulation of the oil and the primary density changes driving it?

A.The oil circulates clockwise because it becomes less dense at the heater and denser at the cooler.
B.The oil circulates clockwise because it becomes denser at the heater and less dense at the cooler.
C.The oil circulates counter-clockwise because it becomes less dense at the heater and denser at the cooler.
D.The oil circulates counter-clockwise because it becomes denser at the heater and less dense at the cooler.
E.The oil does not circulate because the buoyancy forces at the heater and the cooler act on opposite vertical limbs.

Answer: C

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Question 13

1 mark

In a laboratory experiment, a specific liquid is used that exhibits an anomalous density-temperature relationship: for the temperature range between

15^\circ\text{C}

and

30^\circ\text{C}

, the density of the liquid increases as the temperature increases. A deep tank is filled with this liquid at a uniform initial temperature of

15^\circ\text{C}

. Two separate trials are conducted to heat the liquid:

Trial 1: A heating element is placed at the top surface of the liquid.
Trial 2: A heating element is placed at the base of the liquid.

In which trial(s) will significant heat transfer occur via convection throughout the bulk of the liquid while the liquid is within the

15^\circ\text{C}

to

30^\circ\text{C}

range?

A.Trial 1 only
B.Trial 2 only
C.Both Trial 1 and Trial 2
D.Neither Trial 1 nor Trial 2
E.Convection will occur in Trial 2 initially, then switch to Trial 1 once the liquid at the base exceeds $30^\circ\text{C}$ .

Answer: A

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Question 14

1 mark

Two solid objects, a cube of side length

L

and a sphere of radius

L

, are made from the same metal. The cube has a matte black surface and the sphere has a polished silver surface. At any given temperature, the rate of emission of thermal radiation per unit surface area for the matte black surface is

12

times that for the polished silver surface.

Both objects are initially at a temperature of

600\, \text{K}

and are placed in a large evacuated container with walls maintained at

0\, \text{K}

.

What is the ratio of the initial rate of temperature decrease of the cube to that of the sphere?

A.6
B.12
C.18
D.24
E.72

Answer: D

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Question 15

1 mark

An experiment is performed to determine the specific heat capacity of a metal block of mass

2.0\,\text{kg}

. An electric heater with a power rating of

100\,\text{W}

is inserted into the block and switched on for exactly

5

minutes. During this time, the temperature of the block increases from

20\,^\circ\text{C}

to

45\,^\circ\text{C}

. It is estimated that

20\%

of the thermal energy supplied by the heater is lost to the surroundings. What is the specific heat capacity of the metal?

A. $384\,\text{J}\,\text{kg}^{-1}\,^\circ\text{C}^{-1}$
B. $480\,\text{J}\,\text{kg}^{-1}\,^\circ\text{C}^{-1}$
C. $600\,\text{J}\,\text{kg}^{-1}\,^\circ\text{C}^{-1}$
D. $750\,\text{J}\,\text{kg}^{-1}\,^\circ\text{C}^{-1}$
E. $720\,\text{J}\,\text{kg}^{-1}\,^\circ\text{C}^{-1}$

Answer: B

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Question 16

1 mark

A gas is compressed at a constant temperature until it liquefies. In its gaseous state, a sample of the substance occupies a volume

V_{\text{G}} = 2.0\,\text{m}^3

. In its liquid state, the same sample occupies a volume

V_{\text{L}} = 0.002\,\text{m}^3

. Using a simple particle model where the average distance

d

between the centers of adjacent particles is proportional to the cube root of the volume occupied by the sample (

d \propto V^{1/3}

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

\frac{d_{\text{G}}}{d_{\text{L}}}

?

A. $10$
B. $31.6$
C. $100$
D. $1000$
E. $1,000,000$

Answer: A

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Question 17

1 mark

A vertical cylinder containing an ideal gas is sealed by a light, frictionless piston of area

20\,\text{cm}^2

. A

10\,\text{kg}

mass is placed on top of the piston. The cylinder is then submerged in a large tank of water (

ρ = 1000\,\text{kg}\,\text{m}^{-3}

) such that the piston is at a depth of

15\,\text{m}

below the surface. At this depth, the volume of the trapped gas is

400\,\text{cm}^3

. The cylinder is then raised to a shallower depth

h

, and the

10\,\text{kg}

mass is removed from the piston. The volume of the gas increases to

1000\,\text{cm}^3

.

Assume the temperature of the gas and the atmospheric pressure (

1.0 \times 10^5\,\text{Pa}

) remain constant. What is the depth

h

?

(Take

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

)

A.2.0 m
B.4.0 m
C.8.0 m
D.12 m
E.15 m

Answer: A

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Question 18

1 mark

A faulty mercury barometer consists of a uniform vertical glass tube with some air trapped in the space above the mercury column. When the actual atmospheric pressure is

75\,\text{cmHg}

, the height of the mercury column is

65\,\text{cm}

and the air gap above it is

10\,\text{cm}

long. The barometer is moved to a different floor of a building where the mercury column height is observed to be

55\,\text{cm}

.

Assume the temperature remains constant and that air behaves as an ideal gas. What is the actual atmospheric pressure at this new location?

A.50 cmHg
B.55 cmHg
C.60 cmHg
D.65 cmHg
E.75 cmHg

Answer: C

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Question 19

1 mark

A student performs an experiment to find the density of lead shot using the following steps:

1. An empty beaker is placed on a balance and the balance is set to zero.
2. Lead shot is added to the beaker. The balance reading is

452\,\text{g}

.
3. A liquid with a density of

0.80\,\text{g cm}^{-3}

is added to the beaker until the total volume of the lead and liquid is

200\,\text{cm}^3

. The lead shot is completely submerged and the balance reading is

580\,\text{g}

.

What is the density of the lead?

A. $2.26\,\text{g cm}^{-3}$
B. $2.90\,\text{g cm}^{-3}$
C. $5.80\,\text{g cm}^{-3}$
D. $11.3\,\text{g cm}^{-3}$
E. $14.5\,\text{g cm}^{-3}$

Answer: D

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Question 20

1 mark

A car is driving at a constant speed of

u = 0.20v

towards a large stationary vertical wall, where

v

is the speed of sound in air. The car's horn emits a continuous sound of frequency

f_0

.

The sound reflects off the wall and is heard by the driver of the car. Assuming the speed of sound is constant and there is no wind, what is the frequency of the echo heard by the driver in terms of

f_0

?

A. $1.20 f_0$
B. $1.25 f_0$
C. $1.40 f_0$
D. $1.50 f_0$
E. $1.60 f_0$

Answer: D

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Question 21

1 mark

A plane water wave in a ripple tank travels from a deep region into a shallow region. The boundary between the two regions is a straight line.

In the deep region, the wave has a speed of

30\text{ cm s}^{-1}

and a wavelength of

6.0\text{ cm}

. The wave strikes the boundary at an angle of incidence

i

relative to the normal, such that

\sin i = 0.60

.

In the shallow region, the wave speed is

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

.

What are the wavelength

\lambda_s

and the sine of the angle of refraction

\sin r

in the shallow region?

A. $\lambda_s = 4.0\text{ cm}$ and $\sin r = 0.40$
B. $\lambda_s = 4.0\text{ cm}$ and $\sin r = 0.90$
C. $\lambda_s = 9.0\text{ cm}$ and $\sin r = 0.40$
D. $\lambda_s = 9.0\text{ cm}$ and $\sin r = 0.90$
E. $\lambda_s = 4.0\text{ cm}$ and $\sin r = 0.60$

Answer: A

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Question 22

1 mark

A medical ultrasound probe emits a pulse of frequency

2.5\text{ MHz}

into a patient's body. The pulse travels through a fat layer of thickness

3.0\text{ cm}

and then into a muscle layer. The speed of sound in the fat layer is

1500\text{ m s}^{-1}

and in the muscle layer is

1600\text{ m s}^{-1}

. The probe detects an echo reflected from the far side of the muscle layer

100\,\mu\text{s}

after the pulse was emitted.

What is the thickness of the muscle layer and the wavelength of the ultrasound pulse within it?

A.thickness: $4.8\text{ cm}$ ; wavelength: $0.64\text{ mm}$
B.thickness: $4.8\text{ cm}$ ; wavelength: $0.60\text{ mm}$
C.thickness: $6.4\text{ cm}$ ; wavelength: $0.64\text{ mm}$
D.thickness: $4.5\text{ cm}$ ; wavelength: $0.64\text{ mm}$
E.thickness: $9.6\text{ cm}$ ; wavelength: $0.60\text{ mm}$

Answer: A

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Question 23

1 mark

A signal generator produces a sound wave of frequency

400\text{ Hz}

which travels through a long pipe filled with a specific gas. The speed of sound in this gas is

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

. Two microphones are placed inside the pipe at distances of

1.20\text{ m}

and

1.50\text{ m}

from the source.

What is the phase difference between the sound waves at the two microphones, and what type of wave is being detected?

A.phase difference: $135^\circ$ ; type: longitudinal
B.phase difference: $135^\circ$ ; type: transverse
C.phase difference: $45^\circ$ ; type: longitudinal
D.phase difference: $270^\circ$ ; type: longitudinal
E.phase difference: $225^\circ$ ; type: transverse

Answer: A

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Question 24

1 mark

A neutral atom of the nuclide

P

is represented by the notation

^{M}_{Z}P

. A second nuclide

Q

is an ion of an isotope of the same element as

P

. Compared to

P

, the nucleus of

Q

contains 3 more neutrons. The ion

Q

has a charge of

2+

. What is the total number of subatomic particles (protons, neutrons, and electrons) in one ion of

Q

?

A. $M + Z + 1$
B. $M + Z + 5$
C. $M + Z - 2$
D. $M + 3$
E. $M + Z + 3$

Answer: A

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Question 25

1 mark

A radioactive nuclide

^{A}_{Z}X

decays into a stable nuclide

Y

through a sequence of emissions. The sequence consists of exactly two alpha (

\alpha

) particles and a specific number of beta (

\beta^-

) particles. No other particles are emitted. Given that

Y

is an isotope of the original element

X

, which of the following correctly identifies the mass number of

Y

and the number of

\beta^-

particles emitted?

A.mass number of $Y$ : $A - 8$ ; number of $\beta^-$ particles: 4
B.mass number of $Y$ : $A - 8$ ; number of $\beta^-$ particles: 2
C.mass number of $Y$ : $A - 4$ ; number of $\beta^-$ particles: 4
D.mass number of $Y$ : $A - 4$ ; number of $\beta^-$ particles: 2
E.mass number of $Y$ : $A - 8$ ; number of $\beta^-$ particles: 0

Answer: A

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Question 26

1 mark

A nucleus of thorium-232 (

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

) is unstable and decays through a series of steps to reach a stable nucleus of lead-208 (

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

). The only emissions involved in this decay chain are alpha (

\alpha

) and beta-minus (

\beta^-

) particles. What is the total number of particles emitted (the sum of the number of alpha particles and the number of beta-minus particles) during the decay of a single

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

nucleus to

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

?

A. $6$
B. $8$
C. $10$
D. $12$
E. $14$

Answer: C

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Question 27

1 mark

A nucleus of uranium-235 (

^{235}_{92}\text{U}

) undergoes the following sequence of transformations:
1. It emits exactly one alpha (

\alpha

) particle.
2. The resulting nucleus then emits exactly two beta-minus (

\beta^-

) particles.
3. The new nucleus then captures a single neutron (

^1_0n

).
4. Finally, this nucleus undergoes fission, splitting into exactly two identical product nuclei.

What are the atomic number (

Z

) and mass number (

A

) of one of these two identical product nuclei?

A. $Z = 45, A = 115$
B. $Z = 45, A = 116$
C. $Z = 46, A = 115$
D. $Z = 46, A = 116$
E. $Z = 47, A = 116$

Answer: D

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Question 28

1 mark

A student uses a radiation detector to monitor the total count rate from a radioactive source in a laboratory. The background count rate is constant. At

t = 0

, the detector shows a total count rate of

270\text{ counts per minute}

. At

t = 12\text{ minutes}

, the detector shows a total count rate of

90\text{ counts per minute}

. After a long period of time, the count rate recorded by the detector remains constant at

30\text{ counts per minute}

. What is the total count rate shown by the detector at

t = 24\text{ minutes}

?

A.15 counts per minute
B.30 counts per minute
C.45 counts per minute
D.75 counts per minute
E.90 counts per minute

Answer: C

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Question 29

1 mark

A polythene rod is initially neutral. It is rubbed with a dry wool cloth, and as a result,

2.5 \times 10^{12}

electrons are transferred from the cloth to the rod. What is the resulting charge on the rod, and how will it react if it is then brought near a suspended, negatively charged balloon? (The elementary charge is

e = 1.6 \times 10^{-19}\,\text{C}

).

A.Charge: $+4.0 \times 10^{-7}\,\text{C}$ ; Interaction: it attracts the balloon
B.Charge: $-4.0 \times 10^{-7}\,\text{C}$ ; Interaction: it repels the balloon
C.Charge: $-4.0 \times 10^{-7}\,\text{C}$ ; Interaction: it attracts the balloon
D.Charge: $+4.0 \times 10^{-7}\,\text{C}$ ; Interaction: it repels the balloon
E.Charge: $-6.4 \times 10^{-32}\,\text{C}$ ; Interaction: it repels the balloon

Answer: B

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Question 30

1 mark

A metal fuel tanker becomes positively charged while driving due to friction with the air. Before refuelling, a conducting wire is connected between the metal chassis of the tanker and the Earth to discharge it. Which of the following correctly describes the direction of the flow of charge and the reason for this process?

A.Electrons flow from the tanker to the ground to prevent a spark that could ignite fuel vapours.
B.Electrons flow from the ground to the tanker to prevent a spark that could ignite fuel vapours.
C.Protons flow from the tanker to the ground to prevent a spark that could ignite fuel vapours.
D.Electrons flow from the ground to the tanker to generate a current to power the fuel pump.
E.Protons flow from the ground to the tanker to neutralize the excess negative charge.

Answer: B

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ESAT Mock Physics Esat-physics-bank-2

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