Question

A simple pendulum suspended from the roof of a lift oscillated with frequency v when the lift is at rest. If the lift falls freely under gravity, its frequency of oscillation becomes:

• A. zero
• B. v
• C. 2v
• D. infinite

Answer 1

Answer: (A)

zero

Time period of simple pendulum accelerating downward is given by,

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

where,

$l=$ length of the pendulum

$g=$ acceleration due to gravity

$a=$ acceleration of the pendulum

But, when the lift falls freely under gravity, the net acceleration acting on the pendulum will be zero.

$g_{eff}=0⟹T^{\prime }=\infty$

Since the frequency of oscillation is reciprocal of the time period. So,

$⟹frequency=0$

When the lift falls freely, effectively acceleration and frequency of oscillation becomes zero.