Question

A pendulum has a period $T$ for small oscillations. An obstacle $P$ is fixed directly beneath the point of suspension so that only the lower one quarter of the string can follow the pendulum bob when it swings to the left of the equilibrium position. When the pendulum is released from rest as shown, the time it takes to come back to its initial position is:

• A. $T/2$
• B. $3T/4$
• C. $T/4$
• D. $T$

Answer 1

The correct option is B $3T/4$

Time period of a simple pendulum is given by
$T=2\pi \sqrt{\frac{l}{g}}$

Time period for the quarter length of the pendulum is
$T^{\prime }=2\pi \sqrt{\frac{l/4}{g}}=\frac{T}{2}$

Therefore, the total time taken by the pendulum to reach its original position is
$t=\frac{T^{\prime }}{2}+\frac{T}{2}=\frac{T}{4}+\frac{T}{2}=\frac{3T}{4}$
Option B.