A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. In each case, the ball will?

A.

Reach the bottom at the same time

B.

Will take longer time to roll down one plane

C.

Reach the bottom at an unpredictable time

D.

Reach the bottom at the same time and keeps rolling

Answer: Option B

Explanation:

Acceleration of the rolling sphere, a=gsinθ/((1+k^{2}/R^{2})) Velocity of the sphere at the bottom of the inclined plane, v=√(2gh/((1+k^{2}/R^{2}))) The sphere will take a longer time to roll down one plane than the other. It will take a larger time in case if the plane with smaller inclination because the acceleration is proportional to sinθ.

A hook of radius 2m weighs 100kg. It rolls along a horizontal floor so that its centre if mass has a speed of 20cm/s. How much work has to be done to stop it?

A.

5 J

B.

6 J

C.

2 J

D.

4 J

Answer: Option D

Explanation:

v_{cm}=20cm/s = 0.20ms Work required to stop the hoop = Rotational kinetic energy+Traslational kinetic energy Work required = 1/2Iω^{2}+1/2Mv^{2}cm=4J.

Where does the centre of mass of two particles of an equal mass lie?

A.

Inside the body

B.

Outside the body

C.

Near the first body

D.

Midway between them

Answer: Option D

Explanation:

The centre of mass of two particles of equal masses lies midway between them. Its position vector is the average of the position vectors of the two particles.

One solid sphere ‘A’ and another hollow sphere ‘B’ are of same mass and same outer radii. Their moments of inertia about their diameters are respectively IA and IB, such that?

A.

I_{A}=I_{B}

B.

I_{A} is greater thab I_{B}

C.

I_{A} is lesser than I_{B}

D.

I_{A}/I_{B} =ρ_{A}/ρ_{B}

Answer: Option C

Explanation:

In a hollow sphere, the mass is distributed away from the axis of rotation. So, its moment of inertia is greater than that of a solid sphere.