JEE Main · 2021 · 16 Mar 2021 · Shift 1 · Elasticity & SHM

Time period of a simple pendulum is T inside a lift when the lift is stationary. If the lift moves upwards with an acceleration

g /2

, the time period of pendulum will be:

Answer: (A)

Solution

In the frame of the lift the bob feels an effective gravity equal to the true value plus the lift's upward acceleration:

g_{eff} = g + \frac{g}{2} = \frac{3 g}{2}

Since

T = 2 π \frac{L}{g _{eff}}

, the period scales as

\frac{1}{g _{eff}}

T^{'} = T \frac{g}{3 g /2} = \frac{2}{3} T

The new time period is

\frac{2}{3} T

JEE Main · 2021 · 16 Mar 2021 · Shift 1 · Single correct option