Question

Time period of a simple pendulum varies __________ as the square root of the length of the pendulum.

Answer 1

1. A pendulum is a weight suspended from a pivot so that it can swing freely.
2. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position.
3. Time period of a pendulum is given by, $T=2\mathrm{\pi }\sqrt{\frac{\mathrm{L}}{\mathrm{g}}}$ where, $L=lengthofpendulumandg=accelerationduetogravity.$

Hence, time period of a simple pendulum varies directly proportional as the square root of the length of the pendulum.