Question

The mass and diameter of a planet are twice that of the earth. What will be the time period of oscillation of a pendulum on this planet, if it is a seconds pendulum on earth.

• A. $\sqrt{2}$
• B. $2$
• C. $\frac{1}{\sqrt{2}}$
• D. $2\sqrt{2}$

Answer 1

The correct option is A $\sqrt{2}$

Gravitational acceleration, g$\propto M_p$ and g$\propto \frac{1}{r_p^2}$

where $M_p$ is mass of planet and $r_p$ is the radius of the planet

So, $\frac{g_p}{g_e}=\frac{1}{2}$

Time period of pendulum, T$\propto \frac{1}{\sqrt{g}}$

Thus time period of pendulum at the other planet will be $\sqrt{2}$ times its period at earth.

So A is the correct ans