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 the acceleration due to gravity)

Question

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 the acceleration due to gravity), 2 g, 3 g, 4 g, g

MARKS App · Accepted Answer

Time period of a simple pendulum is given by, T = 2 π l g ...(i) When the lift is moving up with an acceleration a , then time period becomes T ′ = 2 π l g + a Here, T ′ = T 2 ⇒ T 2 = 2 π l g + a ...(ii) Dividing Eq.(ii) by Eq. (i), we get a = 3 g

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