Question

A simple pendulum of length $1\,m$ is freely suspended from the ceiling of an elevator. The time period of small oscillations as the elevator moves up with an acceleration of $ 2m/ s^2$ is (use $g = 10m/ s^2$ )

• A. $\frac{\pi}{\sqrt{5}} s $
• B. $\sqrt{\frac{2}{5}} \pi s $
• C. $\frac{\pi}{\sqrt{2}} s $
• D. $\frac{\pi}{\sqrt{3}} s $

Answer 1

Answer: (D)

Given,
Length of simple pendulum $(L)=1 m$
Acceleration $(a)=2 m / s ^{2}$
Gravitation acceleration $(g)=10 m / s ^{2}$
We know that,
$ T=2 \pi \sqrt{\frac{1}{g+a}}=2 \pi \sqrt{\frac{1}{10+2}} $
$=2 \pi \sqrt{\frac{1}{12}}=\pi \sqrt{\frac{4}{12}} $
$I=\frac{\pi}{\sqrt{3}} s$