Question

There is a simple pendulum hanging from the ceiling of a lift. When the lift is stand still, the time period of the pendulum is T. If the resultant acceleration becomes g/4,
then the new time period of the pendulum is [DCE 2004]
A) 0.8 T B) 0.25 T C) 2 T D) 4 T

Answer 1

C is the right option
Hope it helps!!

Answer 2

Answer:

Option (c) 2T

Explanation:

Given,

• Time period of the pendulum when the lift is at rest = T

When the lift is at rest the net acceleration acting on the pendulum is g.

$\therefore T\ =\ 2\pi\sqrt{\dfrac{l}{g}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,eqn (1)$

Where l is the length of the pendulum and g is the gravitational acceleration due to the earth.

Now in the new case, length of the pendulum remains constant and the net acceleration acting on the pendulum is $\dfrac{g}{4}$

Therefore the new time period of the pendulum becomes T'.

$\thefore T'\ =\ 2\pi\sqrt{\dfrac{l}{\dfrac{g}{4}}}\\\Rightarrow T'\ =\ 2\times 2\pi\sqrt{\dfrac{l}{g}$

From the equation (1), we get,

$\therefore T'\ =\ 2T$

Hence the new time period of the pendulum is 2T.