Question

A pendulum has time period $T$ for small oscillations. An obstacle $P$ is situated below the point of suspension $O$ at a distance $\frac{3 l}{4}$ . The pendulum is released from rest. Throughout the motion the moving string makes small angles with vertical. Time after which the pendulum returns back to its initial position is -

• A. $T$
• B. $3 T / 4$
• C. $3 T / 5$
• D. $4 T / 5$

Answer 1

Answer: (B)

first half oscillation is covered with length $l$ and second half with length $\frac{3 l}{4}$ therefore total time can be measured by
$t=\frac{T_{1}}{2}+\frac{T_{2}}{2}_{ \, }$
$T_{1}=2\pi \sqrt{\frac{1}{g}}=T$
$T_{2}=2\pi \sqrt{\frac{1 / 4}{g}}=\frac{T}{2}$
Putting value we get $t=\frac{3 T}{4}$