Description
Medical College Admission Test (MCAT) which is accepted by medical schools in US, Australia, Canada and Carribean Islands for making admission decision.The test assesses candidates critical analysis and reasoning skills, biological and biochemical foundations of living systems, psychological, social and biological foundations of behaviour and chemical and physical foundations of biological systems.
In this collection there will be many samples to practice this test
It will be so important to Medical students who wants to prepare for this test
Study Set Content:
Question 4
A force of 25 N is acting along the North direction and a force of 12 N is acting along the South
direction on a body of mass 1.5 kg. What acceleration will the force bring in the body?
A.
9.87 m/s
2
B.
2.36 m/s
2
C.
4.67 m/s
2
D.
7.67 m/s
2
E.
8.67 m/s
2
Correct Answer: E
Explanation:
A body undergoes acceleration due to an unbalanced force. The unbalanced force here is given as
F = 25 - 12 Or F = 13N
According to Newton’s second law of motion
F = ma -------------- (1)
13 = 1.5 * a
a = 8.67 m/s
2
Therefore, E is the correct answer option.
Question 5
If a wheel is rotating with an angular velocity of 2.5 rad/s, what is the time taken by the wheel to
complete one full rotation?
A.
1.57 s
B.
2.51 s
C.
1.84 s
D.
3.52 s
E.
2.22 s
Correct Answer: B
Explanation:
Time taken to complete one rotation is known as time period. Angular velocity is related to time
period as
ω = 2π/T ---------------- (1)
Putting the values of (π = 3.14) and ω in equation 1 we get
2.5 = (2*3.14)/T
T = 2.51 s
Therefore, B is the correct answer option.
Question 6
An object is to be lifted from the ground to a height of 5m in 25 seconds. If the energy consumed
during the process is 2000 J, what is the power required?
A.
75 J/s
B.
72 J/s
C.
80 J/s
D.
100 J/s
E.
125 J/s
Correct Answer: C
Explanation:
Power is given as
P = W/t ---------------- (1)
Putting the values in equation 1 we get
P = 2000 / 25
P = 80 J/s or Watt
Hence, C is the correct answer option.
Question 7
A block of mass M, connected to a spring of spring constant k (a spring-mass system), is executing
SHM with time period, T on Earth. If the same system executes SHM on the surface of Moon, what
will be the new time period?
A.
More than that on the Earth
B.
Less than that on the Earth
C.
Same as that on the Earth
D.
Zero
E.
Not enough data is provided to predict the answer
Correct Answer: C
Explanation:
Time period is given as
T = 2π √(M/k) ---------------- (1)
At the surface of the Moon, acceleration due to gravity is (1/6)th of that on the surface of the Earth.
As, there is no term related to acceleration due to gravity in equation 1, time period of the system
will remain unaffected. Hence, time period of the system on the moon will be the same as that of
the system on the Earth. Therefore, C is the correct answer option.
Question 8
If the speeds of sound in solid, liquid and gas are arranged in increasing order, which of the
following is a correct arrangement?
A.
Solids< liquids < gas
B.
Liquids < solids < gas
C.
Gas < liquids < solids
D.
Gas < solids < liquids
E.
Liquids < gas < solids
Correct Answer: C
Explanation:
Thespeed of sound in solids like steel and iron is 5000 m/s and 5130 m/s.The speed of sound in
liquidslike water at 0
o
C and 20
o
C is 1402 m/s and 1482 m/srespectively. The speed of sound in air
(gas)at 0
o
C and 20
o
C is 331.5 m/s and 344 m/srespectively. Thus, from the above discussion it can
be concluded that the speed of sound in solids is more than that in liquids and air.
Therefore,thecorrect arrangementfor speeds of soundis air (gas) < liquids < solids. Thus, C is the
correct answer option.
Question 9
What would be the specific gravity of a fluid having density of 944 kg/m
3
?
A.
0.967
B.
0.456
C.
0.944
D.
0.789
E.
0.45
Correct Answer: C
Explanation:
Specific gravity is a dimensionless quantity and is given as
SG = ρ
fluid
/ ρ
water
---------------- (1)
It is quite obvious from equation 1 that specific gravity is a unit less quantity. Putting the values of
densities in equation 1 we get
SG = 944 / 1000 Or SG = 0.944
Therefore, C is the correct answer option.
Question 10
A sample of gas at 313 K occupies a volume of 10 m
3
. What would be its volume at 373 K?
A.
11.92 m
3
B.
15.56 m
3
C.
10.45 m
3
D.
12.67 m
3
E.
Cannot be determined
Correct Answer: A
Explanation:
This question can be solved by applying Charles’s law, which is given as
V
1
/ T
1
= V
2
/ T
2
-------------- (1)
Putting the values in equation 1 we get
10/313 = V
2
/373
V
2
= 11.92 m
3
Therefore, A is the correct answer option.
Question 11
What is the dipole moment between an electron and a proton separated by a distance of 1 nm?
A.
3.8 × 10
-28
Cm
B.
4.5 × 10
-28
Cm
C.
4.5 × 10
-26
Cm
D.
1.6 × 10
-28
Cm
E.
3.2 × 10
-28
Cm
Correct Answer: D
Explanation:
Electric dipole moment between two charges of opposite polarity is given as
p = Qd ----------- (1)
The distance is in nm so we need to convert it into m.
1 nm = 10
-9
m
Putting the values in equation 1 we get
P = 1.6 × 10
-19
× 10
-9
Or, 1.6 × 10
-28
Cm
Hence, D is the correct answer option.
Question 12
For a conductor having a cross section of 2 × 10
-4
m
2
, average drift velocity of the electrons
flowing through it is 10
-3
m/s . If the density of free electrons in the conductor is 6 × 10
-24
m
-3
,
what is the current flowing through the conductor? (Charge on electron = 1.6 × 10
-19
C)
A.
0.45 A
B.
0.045 A
C.
0.27 A
D.
0.31 A
E.
0.19 A
Correct Answer: E
Explanation:
Current flowing through the conductor is given as
I = neAv
d
--------------- (1)
Putting the values in equation 1 we get
I = 6 × 10
24
1.6 × 10
-19
× 2 × 10
-4
× 10
-3
I = 0.19A
Hence, E is the correct answer option.
Question 13
A long straight conductor carries a current of 2 A. What would be the magnetic field at a distance
of 0.05 m from the axis of the conductor? (Permeability of free space is 4π × 10
-7
WbA
-1
m
-1
)
A.
8 × 10
-6
T
B.
4 × 10
-6
T
C.
2.5 × 10
-6
T
D.
1.5 × 10
-6
T
E.
6 × 10
-6
T
Correct Answer: A
Explanation:
Magnetic field due toalong straight conductor is given as
B = [(μ
0
/4π)(2I/a)] -------------- (1)
Putting the values in equation 1 we get
B = (4π × 10
-7
/ 4π) * (2 * 2 / 0.05)
B = 8 × 10
-6
T
Hence, A is the correct answer option.
Question 14
A small water drop on a surface is viewed through a glass. If the real depth of the water drop is 15
cm, what will be the apparent depth of the water drop? (Refractive index of glass =1.5 and
refractive index of air = 1)
A.
5 cm
B.
7.5 cm
C.
8.4 cm
D.
1.5 cm
E.
10 cm
Correct Answer: E
Explanation:
The apparent depth is given as
glass
μ
air
= μ
glass
/ μ
air
= real depth/ apparent depth ---------------- (1)
Putting the values in equation 1 we get
1.5/1 = 15 cm / apparent depth
apparent depth = 10 cm
Hence, E is the correct answer option.
Question 15
Work function of Nickel is 5.01 eV. What is the threshold frequency for Nickel? (Planck’s constant
= 6.6 × 10
-34
Js)
A.
1.21 × 10
15
Hz
B.
0.56 × 10
15
Hz
C.
4.56 × 10
15
Hz
D.
3.67 × 10
14
Hz
E.
2.23 × 10
15
Hz
Correct Answer: A
Explanation:
Threshold frequency is the minimum frequency required to eject photoelectrons out of a material in
photoelectric effect. It is given as
Φ = hv
o
-------------- (1)
Work function is given in eV. So, we need to convert it into Joules.
1 eV = 1.6 x 10
-19
J
5.01 eV = 8.02 x 10
-19
J
Putting the values in equation 1 we get
8.02 x 10
-19
= 6.6 x 10
-34
x v
o
v
o
= 1.21 × 10
15
Hz
Therefore, A is the correct answer option.
Sample paper 3
Question 1
Acceleration of a body is given as
a = (d/t) + (c/t
2
)
(a is acceleration and t is time)
What would be the dimensional formula of d?
A. LT
-1
B. LT
-2
C. L
2
T
-2
D. L
2
T
-1
E. L
-2
T
-2
Correct Answer: A
Explanation:
From dimensional analysis we know that dimensional formula of the left hand side of an expression
should be the same as the dimensional formula of the individual quantities on the right hand side.
Since, SI unit of acceleration is m/s
2
. Therefore, dimensional formula of acceleration becomes LT
-2
. SI
unit of time is s. Therefore, its dimensional formula is T. As said earlier, d/t should have the same
dimensional formula as a. Let dimensional formula of d be X. Hence, it can be written as
LT
-2
= X/T
LT
-1
= X
Hence, dimensional formula for d is LT
-1
. Thus, A is the correct answer option.
Question 2
Which of the following is true for a body having the graph given below?
(v is the velocity and t is time taken)
A. Body at rest
B. Body is accelerating
C. Body is undergoing deceleration
D. Body is undergoing positive acceleration
E. Body is moving with constant speed
Correct Answer: E
Explanation:
The graph given in the question is between velocity and time. Acceleration is time rate of change of
velocity. Velocity is constant here. Therefore, change in velocity is zero and therefore, acceleration is
zero. Thus, options, B, C and D are incorrect. Since, velocity is uniform here, the body cannot be at
rest and so A is an incorrect option. Therefore, E is the correct answer option.
Question 3
Consider the figure given below for a system of two iron blocks connected with a common
pulley. If the block A weighs 200 N, what would be the mass of the iron block B to keep the
whole system in static equilibrium?
A. 20.41 kg
B. 15.57 kg
C. 22.23 kg
D. 34.45 kg
E. 21.45 kg
Correct Answer: A
Explanation:
As the whole system is in static equilibrium, there will be no motion in the blocks. In other words,
weight of both the iron blocks should be the same. Therefore,
Weight of A = Weight of B -------------- (1)
Weight of A = 200 N --------------- (2)
Using 2 in 1 we get
Weight of B = 200 N ------------- (3)
Weight of a body is given as
W = mg -------------- (4)
Putting the values in equation 4 we get
200 = m * 98 Or m = 20.41 kg
Therefore, A is the correct answer option.
Question 4
Which of the following combinations of forces can lead to a resultant unbalanced force of 10
N, if both the forces are acting orthogonally?
A. 4 N and 5 N
B. 6 N and 8 N
C. 5 N and 8 N
D. 8 N and 8 N
E. 5 N and 5 N
Correct Answer: B
Explanation:
Resultant force is given as
R = √( F
1
2
+ F
2
2
+ 2F
1
F
2
cos θ) ------------ (1)
As both the forces are acting orthogonally, θ = 90
o
. Modifying equation 1 we get
R = √( F
1
2
+ F
2
2
+ 2F
1
F
2
cos 90
o
)
Or R = √( F
1
2
+ F
2
2
) ------------- (2)
If we take F
1
= 6 N and F
2
= 8 N and putting the values in equation 2 we get
R = 10N
Putting the values as mentioned in options A, C, D and E, we get the value of the resultant force as
6.4 N, 9.43 N, 11.3 N and 7.07 N.
Thus, for only one combination i.e. 6 N and 8 N we have a resultant force of 10 N.
Hence, B is the correct answer option.
Question 5
If a ferry-wheel completes 100 rotations in 15 s, with what velocity is it rotating?
A. 41.87 rad/s
B. 42.34 rad/s
C. 40.56 rad/s
D. 45.45 rad/s
E. 6.67 rad/s
Correct Answer: A
Explanation:
Velocity with which the ferry-wheel is rotating is its angular velocity. It is given as
ω = [(N * 2π)/ t] ----------------- (1)
Putting the values in equation 1 we get
ω = [(100 * 2π)/ 15] (π = 3.14)
ω = 41.87 rad/s
Therefore, A is the correct answer option.
Question 6
A 5 kg block of ice, kept at some height, has the potential energy of 1000 Joules. What is the
height at which the block has been kept?
A. 20.4 m
B. 21.2 m
C. 10.5 m
D. 11.4 m
E. 24.3 m
Correct Answer: A
Explanation:
Potential energy is given as
PE = mgh ---------------- (1)
Putting the values in equation 1 we get
1000 = 5 * 9.8 * h
h = 20.4 m
Hence, A is the correct answer option.
Question 7
For a body in SHM, the maximum displacement of the body on either sides of the equilibrium
is known as
A. amplitude
B. wavelength
C. period
D. frequency
E. speed
Correct Answer: A
Explanation:
A body in SHM moves under a restoring force. The restoring force is always directed towards the
equilibrium position. Displacement of a body in SHM is measured as the difference between the final
position and the position of equilibrium. Amplitude in SHM is the maximum displacement of the body
from the position of equilibrium. In other words, it can be said that amplitude is the maximum
displacement of the body on either sides of the equilibrium as the body is SHM will continue
performing a to and fro motion. Therefore, A is the correct answer option. Time period or period is the
time taken to complete one cycle of oscillation. Hence, C is an incorrect option. Wavelength is the
distance between two consecutive maxima or minima of a wave. Therefore, B is an incorrect answer
option. Frequency of a body is defined as the number of oscillations about the equilibrium position per
second. Therefore, D is an incorrect option. The magnitude of velocity with which the body in SHM
moves is known as its speed. Therefore, E is an incorrect option.
Question 8
A radio FM is broadcasting signals at a frequency of 400 MHz. What is the wavelength of the
signal, if it is travelling at a speed of 2.5 x 10
8
m/s?
A. 0.534 m
B. 0.625 m
C. 0.725 m
D. 0.918 m
E. 0.025 m
Correct Answer: B
Explanation:
Speed of the wave is given as
v = fλ --------------- (1)
As the frequency is given in MHz, we need to convert it into Hz.
1 MHz = 10
6
Hz
Therefore, 400 MHz = 400 * 10
6
Hz
Putting the values in equation 1 we get
2.5 x 10
8
= 400 * 10
6
* λ
λ = 0.625 m
Therefore, wavelength of the FM signal is 0.625 m and thus, B is the correct answer option.
Question 9
A cubical wooden block of side 0.2 m is floating on the surface of water in such a way that
some part of wooden surface is outside it. What percentage of the wooden surface is outside
the water? (Density of wood = 700 kg/m
3
)
A. 10 %
B. 20 %
C. 25 %
D. 35 %
E. 30 %
Correct Answer: E
Explanation:
This question can be solved by using the formula of specific gravity. Specific gravity tells us whether a
substance will float or sink down in a fluid. It is given as
SG = ρ
body
/ ρ
water
---------------- (1)
Putting the values in equation 1 we get
SG = 700/1000 Or SG = 0.7
Specific gravity provides the fraction of surface of an object inside the fluid. If the specific gravity is
equal to 1, then the object will float with zero percent of the surface outside the fluid. If the specific
gravity is more than 1, then the object will sink completely inside the fluid. Since, specific gravity here
is 0.7, percentage of the wooden surface inside the level of water is
%SG = 0.7 * 100 Or %SG = 70%
Therefore, 70 % of the block is inside the water and 30 % of the block is outside the water.
Hence, E is the correct answer option.
Question 10
20 gram of a substance evaporates at 500 K by absorbing 740 J of energy. If the specific heat
of the substance is 1000 J/kg K, what is the final temperature of the substance?
A. 400 K
B. 413 K
C. 537 K
D. 513 K
E. 637 K
Correct Answer: C
Explanation:
This question can be solved by
Q = mc ΔT ---------------- (1)
As mass is given in grams we need to convert it into kg.
1g = 10
-3
kg
20g = 0.02kg
Change in temperature is given as
ΔT = T
2
- T
1
Putting the values in equation 1 we get
740 = 0.02 * 1000 * (T
2
- 500) Or T
2
= 537 K
Therefore, C is the correct answer option.
Question 11
Potential difference of 150 V is applied across an aluminum conductor of length 2.5 m. If the
density of free electrons in the conductor is 2 x 10
23
m
-3
, what would be the average drift
velocity of the electrons? (Conductivity of aluminum is 3.5 2 x 10
7
Ω
-1
m
-1
and charge on
electron = 1.6 x 10
-19
C)
A. 650.25 m/s
B. 450.65 m/s
C. 656.25 m/s
D. 414.55 m/s
E. 710.23 m/s
Correct Answer: C
Explanation:
Average drift velocity of an electron is given as
v
d
= σE / ne -------------- (1)
Electric field is given as
E = v/l --------------- (2)
Putting the values in equation 2 we get E = 150/2.5 Or E = 60 V/m
Putting the values in equation 1 we get v
d
= [(3.5 x 10
7
* 60) / (2 x 10
25
* 1.6 x 10
-19
)]
Or, v
d
= (2.1 x 10
9
) / 3.2 x 10
6
Or v
d
= 656.25 m.s
Therefore, C is the correct answer option.
Question 12
A beta particle of mass 9.1 x 10
-31
is moving perpendicular to a magnetic field in a region of
0.01 T with a speed of 10
4
m/s. What is the force experienced by the beta particle due to the
magnetic field? (Charge on electron = 1.6 x 10
-19
)
A. 3.2 x 10
-17
N
B. 1.6 x 10
-17
N
C. 4.8 x 10
-17
N
D. 2.4 x 10
-17
N
E. 10
-17
N
Correct Answer: B
Explanation:
Force experienced by the beta particle is given as
F = qvB sin θ ---------------- (1)
As the beta particle is moving perpendicularly to the magnetic field, θ = 90
o
. Charge onabeta particle
is equal to the charge onanelectron; Putting the values in equation 1 we get
F = 1.6 x 10
-19
x 10
4
x 0.01 x sin 90
o
Or, F = 1.6 x 10
-17
* 1 N
Or, F = 1.6 x 10
-17
Hence, B is the correct answer option.
Question 13
A circular coil of radius 0.1 m consists of 10 turns. If the current flowing through the coil is
measured to be 1.5 A, what would be the magnetic field at the center of the coil? (Permeability
of free space is 4π x 10
-7
WbA
-1
m
-1
)
A. 8.5 x 10
-5
T
B. 7.42 x 10
-5
T
C. 9.42 x 10
-5
T
D. 6.32 x 10
-5
T
E. 5.52 x 10
-5
T
Correct Answer: C
Explanation:
Magnetic field at the center of a coil due to the current flowing in it is given as
B = (µ
o
/ 4 π)(2πnI / r) -------------- (1)
Putting the values in equation 1 we get
B = [(4 π x 10
-7
) / 4 π] * [(2π * 10 * 1.5)/0.1]
Or B = 10
-7
* [(2 * 3.14 * 10 * 1.5) / 0.1] (π = 3.14)
Or, B = 10
-7
* 942
Or, B = 9.42 x 10
-5
T
Hence, C is the correct answer option.
Question 14
Refractive index of diamond with respect to air is 2.4 and the refractive index of water with
respect to air is 1.33. What would be the refractive index of diamond with respect to water?
(Refractive index of air = 1)
A. 1.51
B. 0.55
C. 1.8
D. 0.75
E. 0.42
Correct Answer: C
Explanation:
Refractive index of one medium with respect to another medium is given as
2
μ
1
= μ
2
/ μ
1
Here we have been given refractive index of diamond with respect to air = 2.4 i.e.
2.4 = μ
diamond
/1 Or μ
diamond
= 2.4
Also, refractive index of water with respect to air = 1.33 i.e.
1.33 = μ
water
/1 Or μ
water
= 1.33
Thus, refractive index of diamond with respect to water becomes
diamond
μ
water
= 2.4 / 1.33
Or
diamond
μ
water
= 1.80
Thus, C is the correct answer option.
Question 15
What is the Joule equivalent of 1 eV? (Charge on electron = 1.6 x 10
-19
C)
A. 1.6 x 10
-19
J
B. 3.2 x 10
-19
J
C. 3.2 x 10
-13
J
D. 1.6 x 10
-13
J
E. 1 J
Correct Answer: A
Explanation:
Joule is the SI unit of energy. eV is also a unit of energy but for microscopic charged particles. One
electron volt (eV)is defined as the energy possessed by an electron moving in a unit potential field.
We know that energy of a charged particle in a potential field is given as
E = q V J ------------- (1)
For an electronin a potential field of 1 V,energy can be expressed by using equation 1 as
E = e V J ------------- (2)
Putting the value in equation 2 we get
1 ev = 1.6 x 10
-19
* 1 J
Or 1 ev = 1.6 x 10
-19
J
Therefore, A is the correct answer option.
Sample paper 4
Question 1
Which of the following is a dimensionally correct representation for angular momentum?
A. M
2
L
2
T
-1
B. M
2
L
1
T
-1
C. M
2
L
1
T
-2
D. ML
2
T
-1
E. ML
1
T
-1
Correct Answer: D
Explanation:
Angular momentum is given as
L = Iω ------------ (1)
SI unit for I is kgm
2
. Hence, dimensional formula of I becomes ML
2
. Angular velocity is given as
ω = v/ r
SI unit of v is m/s and that of r is m. Hence, SI unit of angular velocity becomes
(m/s)/m Or 1/s
Therefore, dimensional formula of angular velocity is T
-1
. Thus, dimensional formula of angular
momentum from equation 1 becomes
ML
2
/ T Or ML
2
T
-1
Hence, D is the correct answer option.
Question 2
A train at rest starts from station A and travels to station B at a distance of 2 km in 4 minutes?
Consider the following statements.
Instantaneous speed of the train is 8.33 m/s
Average speed of the train is 8.33 m/s
Instantaneous acceleration of the train is 8.33 m/s
2
A.
Which of the following statement(s) is/are true?
B. 1
C. 2
D. 3
E. Both 1 and 3
F. Both 2 and 3
Correct Answer: B
Explanation:
Instantaneous speed of a body is the speed possessed by it at any particular time instant.
Instantaneous speed is a variable and changes accordingly. Speedometer is a device that is used by
the vehicles to know the speed possessed by it at that instant. Average velocity or speed provides
speed of the body for the full journey. It is given as the total distance travelled in total time taken. As in
the question the total time and the total distance are given, hence average speed can be found as
Average speed = Total Distance / Total Time ------------- (1)
Since, distance and time are given in kilometers and minutes we need to convert them Putting the
values in equation 1 we get
Average speed = 8.33 m/s
Instantaneous acceleration is related to instantaneous speed. Hence, instantaneous acceleration
cannot be found here. Thus, B is the correct answer option.
Question 3
A water gallon of mass 500 kg is resting on a horizontal floor. What would be its normal
reaction?
A. 500 N
B. 4900 N
C. 5100 N
D. 250 N
E. 51.02 N
Correct Answer: B
Explanation:
As the water gallon is resting on the floor, normal reaction will be balanced by the weight of the gallon
itself. Therefore,
Normal reaction = Weight of the gallon ------------- (1)
Weight of the gallon is given as
F = mg------------- (2)
Putting the values in equation 1 we get
F = 500 * 9.8 Or F = 4900 N
Using equation 1 we get
Normal reaction = 4900 N
Therefore, B is the correct answer option.
Question 4
A boy of 45 kg jumps out of a window and just before reaching the ground his speed is 2 m/s.
After he hits the ground he stops and the total time taken during this process is 1 s. What is
the force exerted by the ground on the boy?
A. 45 N
B. 22.5 N
C. 180 N
D. 90 N
E. 85 N
Correct Answer: D
Explanation:
According toNewton’s second law of motion, force is time rate of change of momentum and is given
as
F = p / t ------------ (1)
Momentum is given as
p = mv ------------- (2)
Putting the value of m and v in equation 2 we get p = 45 * 2 Or p = 90 kgm/s
Putting the values of p and t in equation 1 we get
F = 90 N
Therefore, D is the correct answer option.
Question 5
A flying disc initially at rest rotates with a constant acceleration. If after 5 s the flying disc has
rotated by 200 radians, what is its angular acceleration?
A. 14 rad/s
2
B. 15 rad/s
2
C. 11 rad/s
2
D. 12 rad/s
2
E. 16 rad/s
2
Correct Answer: E
Explanation:
Here we will apply theequation of rotational motion, which is given as
θ = ω
i
t + (1/2)αt
2
-------------- (1)
Putting the values in equation 1 we get
200 = 0 * t + (1/2) α5
2
α = 400/25
Or α = 16 rad/s
2
Therefore, E is the correct answer option.
Question 6
What would be the efficiency of a motor, if its input power is 500 Joules and the output power
is 100 Joules?
A. 18%
B. 15%
C. 20%
D. 10%
E. 21%
Correct Answer: C
Explanation:
Efficiency of a motor is given as
% η = {P
output
/ P
input
] * 100 -------------- (1)
Putting the values in equation 1, we get
% η = [100 / 500] * 100
Or, % η = 20%
Hence, C is the correct answer option.
Question 7
A body of mass 0.3 kg connected to a spring having a spring constant of 20 N/m is executing
SHM. What is the time period of the SHM?
A. 0.65 s
B. 0.56 s
C. 0.75 s
D. 0.87 s
E. 0.14 s
Correct Answer: C
Explanation:
Time period is given as
T = 2π
√ m / k
-------------- (1)
Putting the values in equation 1 we get T = 2π
√ 0.3 / 20
Or, T = 2 * 3.14 * 0.12 (π = 3.14)
T = 0.75 s
Therefore, C is the correct answer option.
Question 8
Two trains A and B approach a station at 10 m/s and 20 m/s respectively. A stationary observer
in the station can hear the sound of the whistle produced by A only. If the original frequency of
the whistle blown by train A is 300 Hz, what would be the apparent frequency of the sound of
the whistle heard by the observer? (Assume speed of sound in air = 340 m/s)
A. 300 Hz
B. 291.42 Hz
C. 283.33 Hz
D. 318.75 Hz
E. 309.09 Hz
Correct Answer: E
Explanation:
This question can be solved by applying Doppler’s effect for sound waves. Doppler’s effect is related
to change in original frequency of sound if either the source or the observer is moving simultaneously.
Doppler’s effect is given as
f = [(v - v
r
) / (v - v
s
]f
o
-------------- (1)
Putting the values in equation 1 we get f = [(340) / (340-10]*300
f = (34/33)*300
Or f = 309.09 Hz
Therefore, E is the correct answer option.
Question 9
A body in a cubical shape of dimension and having mass of 2 kg is fully immersed in a fluid.
What is the specific gravity of the body?
A. 0.357
B. 0.453
C. 0.564
D. 0.181
E. 0.097
Correct Answer: A
Explanation:
Density is given as
ρ = m/V ------------- (1)
Volume of the body is given as
V = 0.7 * 0.1 * 0.08 Or V = 5.6 x 10
-3
m
3
Putting the values in equation 1 we get
ρ = 2 / 5.6 x 10
-3
Or ρ = 357.14 kg/m
3
Specific gravity is given as
SG = ρ
body
/ ρ
water
---------------- (2)
Putting the values in equation 2 we get
SG = 357.14 / 1000 Or SG = 0.357
Therefore, A is the correct answer option.
Question 10
A heat engine performs work of 10000 J while transferring heat of 12000 J. What is the
efficiency of the engine?
A. 83.3 %
B. 84.5 %
C. 78.6 %
D. 45.7 %
E. 41.6 %
Correct Answer: A
Explanation:
Efficiency of a heat engine is given as
η = W / Q --------------- (1)
Putting the values in equation 1 we get
%η = 10000 / 12000
%η = 0.833 x 100%
Or %η = 83.3 %
Therefore, A is the correct answer option.
Question 11
Two charged particles of charges 4 nC and
– 4 nC are kept 0.2 m cm apart. What is the
magnitude and nature of the electrostatic force? (Permittivity of free space = 8.85 x 10
-12
F/m)
A. -3.6 x 10
-6
N and attractive
B. -2.7 x 10
-6
N and attractive
C. -6.7 x 10
-6
N and attractive
D. -4.5 x 10
-7
N and repulsive
E. 4.5 x 10
-7
N and attractive
Correct Answer: A
Explanation:
Electrostatic force in a region is given as
F = [(1 / 4πε
o
) (q
1
q
2
/ R)] -------------- (1)
Standard value of 1 / 4πε
o
is 9 x 10
9
Nm
2
C
-2
We are given values of charges in nC so we need to convert them into C.
1 nC = 10
-9
C or -4 nC = - 4x10
-9
C
Putting the values in equation 1 we get
F = 9 x 10
9
x [(4 x 10
-9
* 4 x 10
-9
) / 0.2
2
]
Or F = -3.6 x 10
-6
N
As force is negative, that suggests nature of force is attractive.
Hence, A is the correct answer option.
Question 12
What is the current density of electrons flowing through a steel block of length 1 m, if potential
difference applied across the conductor is 200 V? (Conductivity of steel = 1.45 x 10
6
Ω
-1
m
-1
)
A. 2.9 x 10
8
A/m
2
B. 1.4 x 10
8
A/m
2
C. 2.2 x 10
8
A/m
2
D. 3.4 x 10
9
A/m
2
E. 1.45 x 10
4
A/m
2
Correct Answer: A
Explanation:
Current density is given as
J = σE -------------- (1)
Electric field is given as
E = V / l --------------- (2)
Putting the values in equation 2 we get
E = 200/1 Or E = 200 v/m
Putting the values in equation 1 we get
