A simple pendulum is suspended from the ceiling of a lift. When the lift is at rest its time period is T. With what acceleration should the lift be accelerated upwards in order to reduce its period to T / 2 ? (g is acceleration due to gravity)

Step-by-step solution

Time-period of simple pendulum is given as T=2 l g If a be the acceleration of the lift, so that time-period of simple pendulum is reduced to T / 2 . aligned i.e. & T^ =T / 2 2 l g+a &= 1 2 2 l g aligned l g+a = 1 4 , l g g+a=4 g a=3 g