Question

The mass and diameter of a planet are twice those of the earth.what will be the period of oscillation of a pendulum on this planet,if it is a second's pendulum on the earth.

Answer 1

The mass and diameter of a planet are twice those of the earth. what will be the period of oscillation of a pendulum on this planet, if it is a second's pendulum on the earth.

**Answer**

The acceleration due to gravity $g$ on the surface of a planet of radius $R$ and mass $M$ is $= \frac{GM}{R^2}$, where $G$ is the gravitational constant. Therefore, the value of $g$ on a planet of mass and radius twice those of the earth would be half its value on the earth surface. Since the time $T$ of a pendulum varies as $\frac{1}{\sqrt{g}}$, $T$ on the planet will be $\sqrt{2}$ times its value on the earth surface. Hence the desired period of oscillation is $2\sqrt{2}s$.