ESAT Mock Physics ESAT-PHYSICS-MOCK-1: Questions & Worked Solutions

Question 1

1 mark

A neutral plastic rod is rubbed with a dry cloth. During the rubbing process,

5.0 \times 10^{12}

electrons are transferred from the cloth to the rod. What is the resulting charge on the cloth? (The elementary charge is

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

).

A. $-8.0 \times 10^{-7}\,\text{C}$
B. $+8.0 \times 10^{-7}\,\text{C}$
C. $-3.1 \times 10^{-32}\,\text{C}$
D. $+3.1 \times 10^{-32}\,\text{C}$
E. $0\,\text{C}$

Answer: B

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Question 2

1 mark

Three identical metal spheres, X, Y, and Z, are mounted on insulating stands. Sphere X has an initial charge of

+12\,\text{nC}

. Spheres Y and Z are initially neutral (

0\,\text{nC}

). The following sequence of operations is performed:
1. Sphere X is brought into contact with sphere Y and then separated.
2. Sphere Y is then brought into contact with sphere Z and then separated.
What is the final charge on sphere Y?

A. $0\,\text{nC}$
B. $3.0\,\text{nC}$
C. $4.0\,\text{nC}$
D. $6.0\,\text{nC}$
E. $12\,\text{nC}$

Answer: B

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Question 3

1 mark

A aircraft is flying through a storm cloud and becomes electrostaticallly charged due to friction with the air. Before the aircraft is refuelled on the ground, a conducting wire is connected between the aircraft's fuselage and the Earth. Which statement correctly describes the purpose and mechanism of this process?

A.To transfer protons from the ground to the aircraft to balance the charge.
B.To allow excess electrons to flow to or from the Earth, neutralizing the aircraft.
C.To insulate the aircraft from the fuel pump to prevent current flow.
D.To increase the potential difference between the aircraft and the fuel to speed up the flow.
E.To generate a spark in a controlled environment away from the fuel tank.

Answer: B

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Question 4

1 mark

Two long, straight wires are parallel to the

z

-axis in a Cartesian coordinate system. Wire 1 passes through the

xy

-plane at coordinates

(-d, 0)

and Wire 2 passes through the

xy

-plane at

(d, 0)

. Both wires carry an identical current

I

directed into the page (in the

-z

direction). What is the direction of the net magnetic field at the point

(0, d)

in the

xy

-plane?

A.Toward the positive $x$ -axis
B.Toward the negative $x$ -axis
C.Toward the positive $y$ -axis
D.Toward the negative $y$ -axis
E.The net magnetic field is zero

Answer: A

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Question 5

1 mark

A uniform magnetic field

B

is applied at right angles to a straight copper wire of length

L

and diameter

d

. When a potential difference

V

is applied across the ends of the wire, a magnetic force

F

is exerted on it. If the wire is replaced by another copper wire of the same length

L

but with diameter

2d

, and the same potential difference

V

is applied, what is the new magnetic force exerted on the wire? (Assume the resistivity of the copper and the magnetic field remain constant).

A. $\frac{1}{4}F$
B. $\frac{1}{2}F$
C. $F$
D. $2F$
E. $4F$

Answer: E

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Question 6

1 mark

A coil consists of

200

turns of wire. A magnetic field passing through the coil changes such that the magnetic flux increases at a constant rate, inducing an electromotive force (emf) of

4.0\,\text{V}

. If the coil is replaced with one containing

100

turns of wire, and the magnetic flux now increases at four times the original rate, what is the new induced emf?

A. $0.5\,\text{V}$
B. $2.0\,\text{V}$
C. $4.0\,\text{V}$
D. $8.0\,\text{V}$
E. $16.0\,\text{V}$

Answer: D

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Question 7

1 mark

A simple ac generator consists of a coil rotating in a uniform magnetic field. The generator produces an output voltage with a peak value of

V

and a frequency of

f

. If the speed of rotation of the coil is tripled, what are the new peak voltage and the new frequency of the output?

A.Peak voltage is $V$ ; frequency is $3f$
B.Peak voltage is $3V$ ; frequency is $f$
C.Peak voltage is $3V$ ; frequency is $3f$
D.Peak voltage is $9V$ ; frequency is $3f$
E.Peak voltage is $3V$ ; frequency is $9f$

Answer: C

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Question 8

1 mark

A student moves a bar magnet into and out of a stationary coil of wire. The coil is connected to a sensitive ammeter. When the student pushes the North pole of the magnet quickly into the coil, the ammeter shows a momentary deflection of

3\,\text{units}

to the right. Which of the following actions would result in a momentary deflection of more than

3\,\text{units}

to the left?

A.Pulling the North pole out of the coil slowly.
B.Pushing the South pole into the coil more quickly.
C.Pulling the South pole out of the coil more quickly.
D.Holding the North pole stationary inside the coil.
E.Pushing the North pole into the coil more slowly.

Answer: B

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Question 9

1 mark

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

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

for

5.0\,\text{s}

. It then travels at a constant velocity for a further

15.0\,\text{s}

.

What is the average speed of the car for the entire

20.0\,\text{s}

journey?

A. $10.0\,\text{m s}^{-1}$
B. $15.0\,\text{m s}^{-1}$
C. $16.0\,\text{m s}^{-1}$
D. $17.5\,\text{m s}^{-1}$
E. $20.0\,\text{m s}^{-1}$

Answer: D

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Question 10

1 mark

A driver is travelling at a constant speed of

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

on a straight road. They see a hazard and apply the brakes after a reaction time of

0.50\,\text{s}

. The brakes provide a constant deceleration of

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

until the car comes to a complete stop.

What is the total distance travelled by the car from the moment the driver sees the hazard until the car stops?

A. $15\,\text{m}$
B. $75\,\text{m}$
C. $90\,\text{m}$
D. $105\,\text{m}$
E. $165\,\text{m}$

Answer: C

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Question 11

1 mark

Two boxes, A and B, are stacked in a lift as shown. Box A, of mass

5.0\text{ kg}

, sits on top of Box B, of mass

10.0\text{ kg}

. Box B is in contact with the floor of the lift. A light rope attached to Box A exerts a constant upward tension of

30\text{ N}

on Box A. The lift is accelerating downwards at

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

.

What is the magnitude of the normal contact force exerted by Box B on the floor of the lift?
(gravitational field strength

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

)

A.60 N
B.90 N
C.120 N
D.150 N
E.180 N

Answer: B

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Question 12

1 mark

Three blocks, X, Y, and Z, are connected by light inextensible strings and are being pulled vertically upwards. The masses are

m_X = 2.0\text{ kg}

,

m_Y = 3.0\text{ kg}

, and

m_Z = 5.0\text{ kg}

. A pulling force

F = 160\text{ N}

is applied to block X. Each block experiences a constant air resistance (drag) force of

4.0\text{ N}

.

What is the tension in the string connecting block Y and block Z?
(gravitational field strength

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

)

A.54 N
B.74 N
C.78 N
D.84 N
E.106 N

Answer: C

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Question 13

1 mark

A hot air balloon of total mass

1200\text{ kg}

is descending vertically. The burner is adjusted to provide a constant upward upthrust of

10,500\text{ N}

. At a certain instant, the balloon is observed to be accelerating downwards at

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

.

What is the magnitude of the air resistance (drag) acting on the balloon at this instant?
(gravitational field strength

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

)

A.600 N
B.900 N
C.1500 N
D.2100 N
E.2700 N

Answer: B

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Question 14

1 mark

Two light springs,

S_1

and

S_2

, have spring constants

k

and

2k

respectively. A weight

W

is supported by these springs in two different configurations. In Arrangement 1, the springs are connected in parallel. In Arrangement 2, the springs are connected in series. What is the ratio of the total elastic potential energy stored in the springs in Arrangement 2 to the total elastic potential energy stored in Arrangement 1?
(Assume all extensions are within the limit of proportionality for both springs.)

A. $\frac{2}{9}$
B. $\frac{1}{4}$
C.4
D. $\frac{9}{2}$
E.9

Answer: D

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Question 15

1 mark

A specialized elastic component is designed to have a variable stiffness. For extensions between

0

and

0.10\,\text{m}

, it obeys Hooke's law with a spring constant of

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

. For extensions greater than

0.10\,\text{m}

, its stiffness increases such that the additional force required per unit of additional extension is

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

.

What is the total work done to stretch this component from an extension of

0

to a total extension of

0.20\,\text{m}

?
(Assume the component does not exceed its elastic limit.)

A. $4.0\,\text{J}$
B. $5.0\,\text{J}$
C. $6.0\,\text{J}$
D. $8.0\,\text{J}$
E. $12.0\,\text{J}$

Answer: C

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Question 16

1 mark

A solid metal sphere of mass

2.0\,\text{kg}

is dropped from a stationary helicopter at a high altitude. At a certain point during its fall, the sphere has a downward acceleration of

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

. What is the magnitude of the air resistance acting on the sphere at this instant?
(The gravitational field strength

g

is

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

.)

A. $2.0\,\text{N}$
B. $8.0\,\text{N}$
C. $12\,\text{N}$
D. $20\,\text{N}$
E. $28\,\text{N}$

Answer: C

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Question 17

1 mark

A scientific probe has a mass of

120\,\text{kg}

on Earth. It is sent to a planet where the gravitational field strength is

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

. The probe is lowered from a hovering spacecraft onto the planet's surface by a cable at a constant vertical speed of

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

. What is the tension in the cable while the probe is being lowered?
(The gravitational field strength

g

on Earth is

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

.)

A. $120\,\text{N}$
B. $240\,\text{N}$
C. $480\,\text{N}$
D. $1200\,\text{N}$
E. $1680\,\text{N}$

Answer: C

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Question 18

1 mark

An object of mass

4.0\,\text{kg}

is travelling at

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

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

1.0\,\text{kg}

and

3.0\,\text{kg}

respectively. Immediately after the explosion, fragment P is moving at

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

in the original direction of motion of the object. What is the velocity of fragment Q and the increase in the total kinetic energy of the system?

A.velocity of Q: $5.0\,\text{m s}^{-1}$ in original direction; energy increase: $150\,\text{J}$
B.velocity of Q: $5.0\,\text{m s}^{-1}$ in original direction; energy increase: $350\,\text{J}$
C.velocity of Q: $5.0\,\text{m s}^{-1}$ in opposite direction; energy increase: $150\,\text{J}$
D.velocity of Q: $15\,\text{m s}^{-1}$ in original direction; energy increase: $150\,\text{J}$
E.velocity of Q: $15\,\text{m s}^{-1}$ in opposite direction; energy increase: $350\,\text{J}$

Answer: A

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Question 19

1 mark

Two particles, X and Y, both of mass

m

, are moving towards each other in a vacuum. Particle X has speed

u

and particle Y has speed

\frac{u}{2}

. The particles collide head-on. Immediately after the collision, particle X is at rest. What percentage of the initial total kinetic energy of the system is lost during the collision?

A.20%
B.40%
C.50%
D.75%
E.80%

Answer: E

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Question 20

1 mark

A constant resultant force of

4.0\text{ N}

acts on a stationary object of mass

4.0\text{ kg}

as it moves in a straight line along a frictionless horizontal surface. The force acts in the direction of the object's motion for a distance of

8.0\text{ m}

.

What is the final speed of the object?

A. $2.0\text{ m s}^{-1}$
B. $2.8\text{ m s}^{-1}$
C. $4.0\text{ m s}^{-1}$
D. $8.0\text{ m s}^{-1}$
E. $16.0\text{ m s}^{-1}$

Answer: C

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Question 21

1 mark

A wall consists of two layers of material,

X

and

Y

, in perfect thermal contact. Layer

X

has a thickness

d

and thermal conductivity

k

. Layer

Y

has a thickness

3d

and thermal conductivity

2k

. The outer surface of layer

X

is maintained at a constant temperature of

100\,\text{°C}

, and the outer surface of layer

Y

is maintained at

20\,\text{°C}

. Under steady-state conditions, what is the temperature at the interface between the two layers?

A. $32\,\text{°C}$
B. $48\,\text{°C}$
C. $52\,\text{°C}$
D. $60\,\text{°C}$
E. $68\,\text{°C}$

Answer: E

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Question 22

1 mark

A well-insulated copper rod has a length of

80\,\text{cm}

and a cross-sectional area of

2.0\,\text{cm}^2

. One end is held in a steam bath at

100\,\text{°C}

and the other end is embedded in a large block of ice at

0\,\text{°C}

.

Given the following constants:
- Thermal conductivity of copper:

400\,\text{W}\,\text{m}^{-1}\,\text{K}^{-1}

- Specific latent heat of fusion of ice:

3.3 \times 10^5\,\text{J}\,\text{kg}^{-1}

What mass of ice melts in

11

minutes?

A. $0.33\,\text{g}$
B. $2.0\,\text{g}$
C. $20\,\text{g}$
D. $200\,\text{g}$
E. $2000\,\text{g}$

Answer: C

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Question 23

1 mark

A rectangular glass tank is filled with a fluid. A small heating element is placed at the bottom-left corner of the tank, and a cooling block is placed at the top-right corner. Both are switched on simultaneously. Assuming the fluid's density decreases as its temperature increases, which of the following best describes the resulting steady-state convection current and the physical changes driving it?

A.A clockwise circulation is established because fluid density decreases at the heater and increases at the cooling block.
B.A counter-clockwise circulation is established because fluid density decreases at the heater and increases at the cooling block.
C.A clockwise circulation is established because fluid density increases at the heater and decreases at the cooling block.
D.A counter-clockwise circulation is established because fluid density increases at the heater and decreases at the cooling block.
E.No circulation occurs because the density changes at the two corners counteract each other horizontally.

Answer: A

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Question 24

1 mark

Pure water has a maximum density at a temperature of approximately

4^\circ\text{C}

. A deep lake is initially at a uniform temperature of

0^\circ\text{C}

throughout. If the sun begins to warm the surface of the lake, which statement best describes the convective mixing that occurs as the surface temperature increases from

0^\circ\text{C}

to

10^\circ\text{C}

?

A.Convection occurs continuously throughout the process because warmer water is always less dense and rises.
B.Convection occurs only while the surface water is between $0^\circ\text{C}$ and $4^\circ\text{C}$ .
C.Convection occurs only while the surface water is between $4^\circ\text{C}$ and $10^\circ\text{C}$ .
D.No convection occurs because the heat source is at the top of the fluid.
E.Convection occurs only once the surface temperature exceeds $8^\circ\text{C}$ to overcome the initial density of the $0^\circ\text{C}$ water.

Answer: B

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Question 25

1 mark

An electric heater rated at

P = 50\,\text{W}

is used to heat

0.50\,\text{kg}

of a liquid in a vessel. The vessel itself has a heat capacity of

100\,\text{J}\,^\circ\text{C}^{-1}

, and the liquid has a specific heat capacity of

1800\,\text{J}\,\text{kg}^{-1}\,^\circ\text{C}^{-1}

. The liquid is initially at a temperature of

20\,^\circ\text{C}

. Only

80\%

of the energy supplied by the heater is transferred to the liquid and the vessel. How long does it take for the liquid to reach a temperature of

50\,^\circ\text{C}

?

A.540\, $\text{s}$
B.600\, $\text{s}$
C.675\, $\text{s}$
D.750\, $\text{s}$
E.1000\, $\text{s}$

Answer: D

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Question 26

1 mark

Two solid spheres, X and Y, are made of different materials. Sphere Y has a radius twice that of sphere X (

r_Y = 2r_X

). The density of the material in sphere Y is half that of the material in sphere X (

\rho_Y = \frac{1}{2}\rho_X

). The specific heat capacity of the material in sphere Y is three times that of the material in sphere X (

c_Y = 3c_X

). Both spheres are initially at the same temperature and are supplied with the same amount of thermal energy

Q

. What is the ratio of the temperature change of sphere X to the temperature change of sphere Y,

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

?

A.3
B.6
C.12
D.24
E.48

Answer: C

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Question 27

1 mark

A

400\,\text{g}

block of metal at

150\,^\circ\text{C}

is placed into

600\,\text{g}

of oil contained in a calorimeter. The oil and the calorimeter are initially at

20\,^\circ\text{C}

. The calorimeter is made of the same metal as the block and has a mass of

200\,\text{g}

. The final equilibrium temperature of the system is

40\,^\circ\text{C}

. Assuming no heat is lost to the surroundings, what is the ratio of the specific heat capacity of the metal (

c_m

) to the specific heat capacity of the oil (

c_o

)?

A.0.18
B.0.25
C.0.27
D.0.30
E.0.50

Answer: D

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