Question

A simple pendulum of length l hangs from a horizontal roof as shown in figure. The bob of mass $m$ is given an initial horizontal velocity of magnitude $\sqrt{5gl}$ as shown in the figure. The coefficient of restitution $e=\frac{1}{2}$. After how many collisions the bob shall no longer come into contact with the horizontal roof.

Diagram

• A. $4$
• B. $1$
• C. $2$
• D. None of these

Answer 1

The correct option is D None of these

After the collision with horizontal roof:
The speed of the bob after collision $=\frac{1}{2}$ the speed of the bob before collision.

At the highest point the bob has sufficient potential energy to again rise to the level of horizontal roof. Even if the speed of the bob is reduced to zero as a result of collision (after infinite collisions), the bob has sufficient potential energy to again rise to the level of horizontal roof.

Hence, the required number of collisions are infinite.
Final answer: (d)