A simple pendulum of length hangs from a horizontal roof as shown in figure. The bob of mass `m` is given an initial horizontal velocity of magnitude `sqrt(5 gl)` as shown in figure. The coefficient of restitution `e = (1)/(2)`. After how many collisions the bob shall no long come into constant with the horizonrtal roof?

Options

A. 1
B. 2
C. 4
D. none of these

Answer

A

Explanation

After the collision with horizontal roof:
The speed of the both after collision `= (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 collision), the bob has sufficient potential energy to again rise t the level to horizontal roof.
Hence the required number of collision are infinite.