Question

A simple pendulum is first allowed to swing freely on Earth and then taken to the moon. Which of the following statements about the pendulum is correct?

• A. The period of the pendulum on the moon is greater than it was on Earth
• B. The frequency of the pendulum on the moon is greater than it was on Earth
• C. The potential energy of the pendulum on the moon is greater than it was on Earth
• D. The kinetic energy of the pendulum on the moon is greater than it was on Earth
• E. The period, the frequency, the kinetic energy, and the potential energy of the pendulum on the moon are the same as they were on Earth

Answer 1

The correct option is A The period of the pendulum on the moon is greater than it was on Earth

We know the time period of a simple pendulum is given by

$T=2\pi \sqrt{\frac{l}{g}}$ where $l=$effective length of pendulum and $g=$ gravitational acceleration

or $T\propto \sqrt{\frac{1}{g}}$

It means when $g$ decreases ,$T$ will increase and vice-versa, as we know value of $g$ is smaller on moon than earth therefore period $T$ of pendulum will be greater on moon than earth.