Question

A vehicle is moving on a circular path of radius $R$ with speed $\sqrt{gR}$. A simple pendulum of length, $l$, hangs from the ceiling of the vehicle. The time period of small oscillations of the pendulum is

[where $l<<R$]

• A. $2\pi \sqrt{\frac{l}{g}}$
• B. $2\pi \sqrt{\frac{l}{\sqrt{2}g}}$
• C. $2\pi \sqrt{\frac{\sqrt{2}l}{g}}$
• D. None of the above

Answer 1

The correct option is B $2\pi \sqrt{\frac{l}{\sqrt{2}g}}$

Pendulum is observed w.r.t. vehicle's frame
$g_{eff}=\sqrt{g^2+g^2}=\sqrt{2}g$

$T=2\pi \sqrt{\frac{l}{g_{eff}}}=2\pi \sqrt{\frac{l}{\sqrt{2}g}}$

$T=2\pi \sqrt{\frac{l}{\sqrt{2}g}}$