Question

A pendulum makes perfectly elastic collision with block of $m$ lying on a frictionless surface attached to a spring of force constant $k$. Pendulum is slightly displaced and released. Time period of oscillation of the system is

• A. $2\pi [\sqrt{\frac{l}{g}}+\sqrt{\frac{m}{k}}]$
• B. $\pi [\sqrt{\frac{l}{g}}+\sqrt{\frac{m}{k}}]$
• C. $2\pi \sqrt{\frac{l}{g}}$
• D. $2\pi \sqrt{\frac{m}{k}}$

Answer 1

The correct option is B $\pi [\sqrt{\frac{l}{g}}+\sqrt{\frac{m}{k}}]$

As pendulum is released for the half of pendulums time period. It will perform SHM and after striking the block, the block will perform half SHM ie, both the block and pendulum will perform half SHM.

So final time period,

$T=\pi \sqrt{\frac{l}{g}}+\pi \sqrt{\frac{m}{k}}T=\pi [\sqrt{\frac{l}{g}}+\sqrt{\frac{m}{k}}]$