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 lift be accelerated upwards in order to reduce its time period to T/2?

• A. -3g
• B. g
• C. 2g
• D. 3g

Answer 1

The correct option is D 3g

We know $T=2\pi \sqrt{\frac{l}{g}}$.
Thus, T is inversely proportional to square root of g.
For, time period to become T/2, we have $g_{eff}=4g$ beacause $2\pi \sqrt{\frac{l}{4g}}=T/2$
Thus, to get $g_{eff}=4g$, lift should be moving upward with $3g$, so that net acceleration of pendulum should be $3g$(downward due to pseudo force)+$g$(downward due to gravity)=$4g$