A simple pendulum is suspended from ceiling of a lift when lift is at rest its period is 'T'. With what acceleration 'a' should lift be accelerated upward in order to reduce the period to ' T 2 ? (take 'g' as acceleration due to gravity)

Step-by-step solution

The period of a simple pendulum is T = 2 L g_ eff , where L is the length and g_ eff is the effective gravitational acceleration. When the lift is at rest, g_ eff = g , so the period is T = 2 L g . If the lift accelerates upward with acceleration a , the effective gravity becomes g + a , yielding a new period T' = 2 L g + a . Given that T' = T 2 , substitute the expressions: 1 2 2 L g = 2 L g + a Simplify and square both sides: L g = 4 L g + a Cancel L and solve for a : g + a = 4g a = 3g The lift must accelerate up