Question

A cart is falling freely under gravity. Find the time period of a simple pendulum attached to its ceiling.

• A. $\text{Zero}$
• B. $1\text{s}$
• C. $2\text{s}$
• D. $\infty$

Answer 1

The correct option is D $\infty$

For a freely falling body,
$a=g$, along downwards direction.
Effective value of acceleration due to gravity is,
$\Rightarrow g^{\prime }=g-a=g-g=0$
$\Rightarrow$Time period of pendulum will be:
$T=2\pi \sqrt{\frac{l}{g^{\prime }}}$
$T=2\pi \sqrt{\frac{l}{0}}=\infty$
$\therefore T\to \infty$
Hence option $\left(d\right)$ is correct.