Question

A pendulum is suspended in a lift and its period of oscillation when the lift is stationary is $T_{0}.$ What must be the acceleration of the lift for the period of oscillation of the pendulum to be $\frac{T_{0}}{2}?$

• A. $2g$ downward
• B. $2g$ upward
• C. $3g$ downward
• D. $3g$ upward

Answer 1

Answer: (D)

$T_{0}=2\pi \sqrt{\frac{\ell }{g}}$
$\frac{T_{0}}{2}=2\pi \sqrt{\frac{\ell }{g + a}}$
$\frac{\sqrt{\frac{\ell }{g}}}{2}=2\pi \sqrt{\frac{\ell }{g + a}}$
$\frac{1}{4 g}=\frac{1}{ g + a}$
$g+a=4g$
$a=3g$ upward