# Engineering Physics Questions and Answers – Significance of Moment of Inertia

This set of Basic Engineering Physics Questions and Answers focuses on “Significance of Moment of Inertia”.

1. A cylinder rolls up an inclined plane, reaches some height and then rolls down (without slipping throughout these motions). The direction of the frictionless force acting on the cylinders is ___________
a) Up the incline, while ascending and down the incline, while descending
b) Up the incline, while ascending as well as descending
c) Down the incline, while ascending and up the incline, while descending
d) Down the incline, while ascending as well as descending

Explanation: Whether the cylinder rolled up or down, the centre of mass and hence the point of contact of the cylinder has an acceleration g sinθ in the downward direction. Hence in both cases, the force of friction acts up the inclined plane.

2. A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same, which one of the following will not be affected?
a) Moment of inertia
b) Angular momentum
c) Angular velocity
d) Rotational kinetic energy

Explanation: As the radius increases, the moment of inertia of the sphere increases. As no external torque acts in free space, the speed of rotation decreases but the angular momentum remains constant.

3. A thin circular ring of mass m and radius R is rotating about its axis with a constant angular velocityω. Two objects each of mass M are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity ω, which is equal to?
a) mω/(m+M)
b) mω/(m+2M)
c) ((m+2m)ω)/m
d) ((m-2M)ω)/((m+2M))

Explanation: By conservation of angular momentum,
(m+2M)R2 ω=mR2 ω
ω=mω/(m+2M).

4. A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then, maximum acceleration down the plane is for (No rolling) is ___________
a) Solid sphere
b) Hollow sphere
c) Ring
d) All same

Explanation: As the bodies slide and do not roll, they all have the same acceleration, a=gsinθ.

5. In a bicycle the radius of rear wheel is twice the radius of the front wheel. If rf and rr are the radii vf and vr are the speeds of top most points of wheels, then?
a) vr=2vf
b) vf=2vr
c) vr=vf
d) vr is lesser than vf

Explanation: Speeds of the top most points of both wheels will be equal and equal to that of centre of mass of the car.
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6. Two rings of radii R and nR made from the same wire have the ratio of moments of inertia about an axis passing through their centre equal to 1:8. What is the value of n?
a) 2
b) 2√2
c) 4
d) ½

Explanation: As the radius of the second ring is n times, length and hence the mass of wire used is also n times.
I1/I2 = (MR2)/(nM(nR)2)=1/n3 = 1/8
Therefore, n=2.

7. In an orbital motion, the angular momentum vector is ___________
b) Parallel to the linear momentum
c) In the orbital plane
d) Perpendicular to the orbital plane

Explanation: In an orbital motion, the direction of the angular momentum vector is perpendicular to the orbital plane.

8. If there is a change of angular momentum from J to 4J in 4s, then the torque is ___________
a) (3/4) J
b) 1J
c) (5/4) J
d) (4/3) J

Explanation: τ=dL/dt
τ=(4J-J)/4=3/4 J.

9. A horizontal platform is rotating with uniform angular velocity ω around the vertical axis passing through its centre. At some instant of time, a viscous liquid of mass m is dropped at the centre and is allowed to spread pout and finally fall. The angular velocity during this period ___________
a) Decreases continuously
b) Decreases initially and increases again
c) Remains unaltered
d) Increases continuously

Explanation: By conservation of angular momentum,
L = Iω = constant
As the liquid is dropped, it starts spreading out. The moment of inertia increases and angular velocity decreases. As the liquid starts falling, the moment of inertia again decreases and the angular velocity increase.

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