Question

A simple pendulum of length $1m$ 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)

$\frac{\pi }{\sqrt{3}}s$

Time period of the pendulum $T=2\pi \sqrt{\frac{l}{g_{eff}}}=2\pi \sqrt{\frac{l}{g+a}}$
Given : $a=2m/s^2$ $l=1m$
$T=2\pi \sqrt{\frac{1}{10+2}}=\frac{\pi }{\sqrt{3}}s$