Q. 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}
 Answer: D

Explaination: Explanation: Angular momentum is given as
L = I ω  (1)
SI unit for I is kgm^{2}. Hence, dimensional formula of I becomes, Angular velocity is given as
ω = v/r
SI unit of v is m/s and v 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.
Q. 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.
1. Instantaneous speed of the train is 8.33 m/s
2. Average speed of the train is 8.33 m/s
3. Instantaneous acceleration of the train is 8.33 m/s^{2}
Which of the following statement(s) is/are true?
1. Instantaneous speed of the train is 8.33 m/s
2. Average speed of the train is 8.33 m/s
3. Instantaneous acceleration of the train is 8.33 m/s^{2}
Which of the following statement(s) is/are true?
 a. 1
 b. 2
 c. 3
 d. Both 1 and 3
 e. Both 2 and 3
 Answer: B

Explaination: 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 equation 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.
Q. 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
 Answer: B

Explaination: Explanation: As the water gallon id 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.
Q. 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
 Answer: D

Explaination: Explanation: According to Newton’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 values of m and v in equation 2 we get
p = 45*2 Or, p = 90 kg m/s
Putting the values of p and t in equation 1 we get
F = 90 N
Therefore, D is the correct answer option.
Q. 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}
 Answer: E

Explaination: Explanation: Here we will apply the equation of rotational motion, which is given as
ϴ = ω_{i} t + (1/2)at^{2}  (1)
Putting the values in equation 1 we get
200 = 0 * t +(1/2) a * 5^{2}
a = 400/25
Or, a = 16 rad/s^{2}
Therefore, E is the correct answer option.
Q. 6
What would be the efficiency of a motor, if its input power is 500 Joules and output power is 100 Joules?
 a. 18 %
 b. 15 %
 c. 20 %
 d. 10 %
 e. 21 %
 Answer: C

Explaination: Explanation: Efficiency of a motor is given as
%η = (P_{output}/P_{input})*100  (1)
Putting the values in equation 1, we get
%η = (500/100)*100
Or, %η = 20%
Hence, C is the correct answer option.
Q. 7
A body of mass 0.3 kg connected to a spring having 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
 Answer: C

Explaination: Explanation: Time period is given as
T = 2π√(m/k)  (1)
Putting the values in equation 1 we get
T = 2 π √(0.3/20)
Or, T = 2 * 3.14 * 0.12 (π = 3.14)
T = 0.75 s
Therefore, C is the correct answer option.
Q. 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
 Answer: E

Explaination: 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 = [(vv_{r}) / (vv_{s})]f_{o}  (1)
Putting the values in equation 1 we get
f = [300/(34010)]*300
f = (34/33)*300
Or, f = 309.09 Hz
Therefore, E is the correct answer option.
Q. 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
 Answer: A

Explaination: Explanation: Density is given as
p = m / v  (1)
Volume of the body is given as
v = 0.75*0.1*0.08
Or, V = 5.6*10^{3} m^{3}
Putting the values in equation 1 we get
p = 2/(5.6*10^{3})
Or, p = 357.14 kg/m^{3}
Specific gravity is given as
SG = P_{body} / P_{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.
Q. 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 %
 Answer: A

Explaination: Explanation: Efficiency of heat engine is given as
η = W/Q  (1)
Putting the values in equations 1 we get
η = 10000/12000
% η=0.833*10%
Or, % η= 83.3%
Therefore, A is the correct answer option.
Q. 11
Two charged particles of charge 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*10^{12} F/m)
 a. 3.4 * 10^{6} N and attractive
 b. 2.7 * 10^{6} N and attractive
 c. 6.7 * 10^{6} N and attractive
 d. 4.5 * 10^{7} N and repulsive
 e. 4.5 * 10^{7} N and attractive
 Answer: A

Explaination: Explanation: Electrostatic force in a region is given as
F = [1/(4πε_{o})]*[q_{1}q_{2} / R^{2}]  (1)
Standard value of F = 1/(4πε_{o}) is 9*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 = 4 * 10^{9} C
Putting the values in equation 1 we get
F = 9 * 10^{9} * {[4*10^{9}*4*10^{9}] / 0.2^{2}}
Or, F = 3.6*10^{6} N
As force is negative, that suggests nature of force is attractive.
Hence, A is the correct answer option.
Q. 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*10^{6} Ω^{1}m^{1})
 a. 2.9 * 10^{8} A/m^{2}
 b. 1.4 * 10^{8} A/m^{2}
 c. 2.2 * 10^{8} A/m^{2}
 d. 3.4 * 10^{9} A/m^{2}
 e. 1.45 * 10^{4} A/m^{2}
 Answer: A

Explaination: Explanation: Current density is given as
J = σE  (1)
Electric field is given as
E = V/I  (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
J = 1.45*10^{6}*200
Or, J = 2.9*10^{8} A/m^{2}
Hence, A is the correct answer option.
Q. 13
A solenoid of length 60 cm and radius 2.4 cm carries current of 3 A. If the number of turns is 400, what is the magnetic field at the center of the solenoid on its axis? (Permeability of free space is 4π*10^{7} WbA^{1}m^{1})
 a. 2.5 * 10^{3} T
 b. 1.5 * 10^{3} T
 c. 4.5 * 10^{4} T
 d. 5.2 * 10^{4} T
 e. 1.8 * 10^{4} T
 Answer: A

Explaination: Explanation: Magnetic field at the center of a solenoid is given as
B = μ_{o}nI / I  (1)
As length is given in cm we need to convert it into m.
1 cm = 10^{2} m
60 cm = 0.6 m
Putting the values in equation 1 we get
B = (4π*10^{7}*400*3) / 0.6 (π = 3.14)
Hence, A is the correct answer option.
Q. 14
What would be the minimum angle of incidence so that a ray of light travelling from medium 1 of refractive index 1.7 to medium 2 of refractive index 1.5 does not emerge out of medium 2?
 a. sin^{1}(0.88)
 b. cos^{1}(0.88)
 c. tan^{1}(0.88)
 d. tan^{1}(1.13)
 e. sin^{1}(1.13)
 Answer: A

Explaination: Explanation: For a ray of light incident on a medium to not emerge from it is known as limiting case of total internal reflection. For the minimum angle the refracted ray travels along the interface. For the incident ray making an angle more than the minimum angle the ray will reflect back and this is known as total internal reflection. From Snell’s law we have
μ_{1} sin ϴ_{i} = μ_{2} sin ϴ_{r}  (1)
Putting the values in equation 1 we get
1.7*sin ϴ_{i} = 1.5*sin90^{0}
ϴ_{i} = sin^{1}(0.88)
Therefore, A is the correct answer option.
Q. 15
A photon of frequency 350 GHz is incident on a metal surface. What is the energy of the photon is eV? (Plank’s constant = 6.6*10^{34} Js)
 a. 2.34*10^{3} eV
 b. 1.24*10^{2} eV
 c. 1.44*10^{3} eV
 d. 3.46*10^{2} eV
 e. 0.45 eV
 Answer: C

Explaination: Explanation: Energy possessed by a photon is given as
E = hv  (1)
Frequency is given in GHz so, we need to convert it into Hz.
1 GHz = 10^{9} Hz
350 GHz = 3.5*10^{11} Hz
Putting the values in equation 1 we get
E = 6.6*10^{34}*3.5*10^{11}
Or, E = 2.31*10^{22} J
We need to convert energy in Joules into eV as given below
1.6*10^{19} J = 1 eV
1 J = [1 / (1.6*10^{19})]eV
Or, 2.31*10^{22} J = 1.44 * 10^{3} eV
Therefore, a photon with frequency of 350 GHz has energy of. Hence, C is the correct answer option.