A hollow sphere of mass m and radius  R is rolling downward on a rough inclined plane of inclination  0 (theta) . if the coefficient of friction between  the hollow sphere and incline is µ then

 

1. Friction opposes its translation

2. Friction supports rotation motion

3. on decreasing  0 (theta), frictional force decreases

4. all of these.

 

Pleae provide justification

The answer to this is 4.all of these.

 

When a body is placed on an inclined plane at an angle θ, it tries to slip down and hence a static friction 'f' acts upwards. Thus it opposes the translational motion. This friction provides a torque which causes the body to rotate.Frictional force provides the torque for rotation. Hence we can say that the friction supports rotational motion.

If μ is the minimum coefficient of friction between  the hollow sphere and the incline plane .From the motion of hollow sphere we can write that

mg sin θ - f =ma

where a is the acceleration along the incline plane(i.e. tangential acceleration of the rolling sphere)

f - static friction acting upwards

θ- inclination angle.

From all the above we can say that the frictional force decreases on decreasing θ.