1. Moment of inertia can be regarded as the measure of the rotational inertia of the body.
a) True
b) False
Explanation: The mass of a body resists change in its state of linear motion, it is a measure of its inertia in linear motion, Similarly, the moment of inertia of a body about an axis of rotation resists a change in its rotational motion. The greater the moment of inertia of body, the greater is the torque required to change its state of rotation. Thus moment of inertia of a body can be regarded as the measure of the rotational inertia of the body.
2. The flying wheel attached to the shaft of steam engine works on the principle of ___________
a) Centripetal action
b) Moment of inertia
c) Newton’s third law of motion
d) Conservation of momentum
Explanation: A flywheel is attached to the shaft of an engine. Because of its large moment of inertia, the flywheel opposes the sudden increase or decrease in the speed of the vehicle. It allows a gradual change in the speed and prevents jerky motions and hence ensures a smooth ride for the passengers.
3. A wheel of mass 8kg and radius of gyration 25cm is rotating at 300rpm. What is its moment of inertia?
a) 0.5 kgm2
b) 10 kgm2
c) 5 kgm2
d) 0.25 kgm2
Explanation: M = 8kg, K = 25cm = 0.25m
Therefore, l = MK2 = 8×0.252 = 0.5 kgm2.
4. The moment of inertia of a uniform circular disc about its diameter is 100gcm2. What is its moment of inertia about its tangent?
a) 200 gcm2
b) 100 gcm2
c) 900 gcm2
d) 500 gcm2
Explanation: By the theorem of parallel axes, moment of inertia about a tangent parallel to the diameter,
I = Id+MR2 = 1/4 MR2+MR2=5/4 MR2
I = 5×100 = 500 gcm2.
5. The moment of inertia of a uniform circular disc about its diameter is 100 gcm2. What is its moment of inertia about an axis perpendicular to its plane.
a) 500 gcm2
b) 100 gcm2
c) 200 gcm2
d) 700 gcm2
Explanation: By theorem of perpendicular axes, moment of inertia of the disc about an axis perpendicular to its plane,
I = Sum of the moments of inertia about two perpendicular diameters
I = Id+Id=2×1/4×MR2=2×1000= 200 gcm2.
6. Calculate the moment of inertia of the earth about its diameter, taking it to be a sphere of 1025kg and diameter 12800km.
a) 1.64 kgm2
b) 16.4×1038 kgm2
c) 1.64×1038 kgm2
d) 0
Explanation: M = 1025kg, R = 6400km = 6.4×106 m
Moment of inertia of the earth about its diameter I = 2/5 MR2 = 2/5×1025×(6.4×106)2
I = 1.64×1038 kgm2.
7. A torque of 2×10-4 Nm is applied to produce an angular acceleration of 4rad/s2 in a rotating body. What is the moment of inertia of the body?
a) 0.5 kgm2
b) 5×104 kgm2
c) 0.5×10-4 kgm2
d) 0.5×104 kgm2
Explanation: Torque = Iα
I = Torque/α = (2×10-4)/4=0.5×10-4 kgm2.
8. A boy carrying a box on his head is walking on a level load from one place to another on a straight road is doing no work. The statement is?
a) Correct
b) Incorrect
c) Partly correct
d) Insufficient data
Explanation: The body applies force on the load in the upward direction. The displacement of the load is in the horizontal direction.
9. Kinetic energy with any reference must be ___________
a) Zero
b) Positive
c) Negative
d) Either negative or positive
Explanation: KE = 1/2 mv2
It is always positive.
10. The kinetic energy of a body becomes four times of its initial value, then new momentum will ___________
a) Become twice its initial value
b) Become thrice its initial value
c) Become four times its initial value
d) Remains constant
Explanation: p = √2mK
p‘ = √(2m×4K) = 2√2mK = 2p
If the kinetic energy of a body becomes four times of its initial value, then new momentum will become twice its initial value.