Question

Question #6578f

Answer 1

For a simple pendulum making a small angle `theta` with the vertical we have its time period `T`, the time taken for a complete cycle as

`T=2pisqrt(l/g)`
where `l` is its length and `g` is acceleration due to gravity.

Setting `T=oo`, we get

Either `l=oo` or `g=0`.
Physically it may not be possible to realize a pendulum with `l` length as infinite.
However, there would arise situations where `g=0`. Though division by `0` is not defined we may be able to state that time period will be a very large undefined number.
it is same as running a pendulum in gravity free region,

Pendulum in a freely falling lift is an example of such a situation. In the frame of reference of lift we need to account for acceleration of so that so that Newton's Laws of motion are valid and could be applied. Hence, a pseudo force equal and opposite to downward force due to `g` is added to acceleration of the lift.