Question

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

• A. $2\pi \sqrt{\frac{\ell }{g}}$
• B. $2\pi \sqrt{\frac{\ell }{\sqrt{2}g}}$
• C. $2\pi \sqrt{\frac{\sqrt{2}\ell }{g}}$
• D. None of these

Answer 1

Answer: (B)

$2\pi \sqrt{\frac{\ell }{\sqrt{2}g}}$

Answer is B
We know that time period of pendulum is
$T=2\pi \sqrt{\frac{l}{g_r}}$
Now,
$g_r=\sqrt{g^2+g^2}$
Therefore,
$T=2\pi \sqrt{\frac{l}{\sqrt{2}g}}$