1. 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.
2. 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).
3. 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.
4. 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.
5. 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.
6. In an orbital motion, the angular momentum vector is ___________
a) Along the radius vector
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.
7. 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.
8. 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.
9. When force and displacement are in the same direction, the kinetic energy of the body ___________
a) Increases
b) Decreases
c) Remains constant
d) Becomes zero
Explanation: When force and displacement are in the same direction, the kinetic energy of the body increases. The increase in kinetic energy is equal to the work done on the body.
10. The momentum of a body of mass 5kg is 500kgm/s. Find its kinetic energy?
a) 2×105 J
b) 2.5×104 J
c) 2.5×105 J
d) 2.5J
Explanation: Kinetic energy = p2/2m = 5002/(2×5)
Kinetic energy = 2.5×104 J.