Question

A solid cylinder rolls without slipping on a rough horizontal floor, its center of mass is moving with a speed $v$. It makes an elastic collision with smooth vertical wall. After impact

• A. Its center of mass will move with a speed $v$ initially.
• B. Its motion will be rolling without slipping immediately.
• C. Its motion will be rolling with slipping initially, and its rotational motion will stop momentarily at the same instant.
• D. Its motion will be rolling without slipping only after some time.

Answer 1

Answer: (A), (C), (D)

Its motion will be rolling without slipping only after some time.


Given, the initial velocity of the solid cylinder is $v$ and collision between the solid cylinder and the vertical wall is elastic collision in nature.


Let the velocity of the solid cylinder just after the collision be $v^{\prime }$.

$\therefore v^{\prime }=ev=v[\because e=1]$

Since, the vertical wall is smooth, hence due to the absence of any tangential force there will be no torque, so the angular velocity will remain unchanged.

Now, velocity of point $\text{O}$ just after impact, $v_o=2v$ (opposite to its initial direction). Hence, it is rolling as well as slipping.

The friction will act in opposite direction and after some time slipping will stop, and after that pure rolling will take place, when $v=r\omega$.

$\Rightarrow$ Velocity of point $\text{O}$, $v_o=0$

Hence, pure rolling is occurring.


Hence, $\text{(A), (C)}$ and $\left(\text{D}\right)$ is the correct answer.

Why this question ? Key concept: The point of contact of a rotating body with ground should have zero velocity for the motion to be called pure rolling, otherwise it is rolling + slipping together. The friction will act in such a way that it will start pure rolling.