Question

A simple pendulum attached to ceiling of lift has time period T when lift is at rest. Find its time period of lift if it starts accelerating upwards with acceleration g/2?

1. $\sqrt{\frac{2}{3}}T$ 
2. $\frac{\sqrt{2}}{3}T$ 
3. $\frac{2}{\sqrt{3}}T$
4. $\frac{T}{3}$

Answer 1

The correct option is 1) $\sqrt{\frac{2}{3}}T$ 

$T=2\pi \frac{l}{g}$ 

$T^{\prime }=2\pi \frac{l}{g+\frac{g}{2}}$ 

$\therefore \frac{T^{\prime }}{T}=\sqrt{\frac{g}{\frac{3g}{2}}}$ 

$T^{\prime }=T\frac{\sqrt{2}}{3}$