Question

In the situation given, a force $F$ is applied at the top of sphere. Study following statements.

• A. The sphere will move faster if friction is absent.
• B. The sphere will move faster if friction is present.
• C. The sphere will move with the same velocity irrespective the friction
• D. Friction supports the motion.

Answer 1

Answer: (B), (D)

The correct options are
B The sphere will move faster if friction is present.
D Friction supports the motion.

Let there is no friction initially.

${\tau }_o=I\alpha$

$FR=\frac{2}{5}M{R}^2\alpha ⟹R\alpha =\frac{5F}{2M}$

Also $F=Ma$

Thus acceleration of point A, $a_A=\alpha R-a=\frac{3F}{2M}$ in the backward direction, i.e point A tends to slide backwards and hence friction force will act in forward direction.

When friction is present, acceleration of point O $a_f=\frac{F+f}{M}>a$

Thus frictional force supports the motion and the sphere will move faster in its presence.