Q. A clock $S$ is based on oscillation of a spring and clock $P$ is based on pendulum motion. Both clock run at the same rate on earth. On a planet having the same density as earth but twice the radius,
A) $S$ will run faster than $P$
B) $P$ will run faster than $S$
C) Both will run at the same rate as on the earth
D) Both will run at the same rate which will be different from that on the earth
Explanation
(b) $g = \frac{GM}{R^{2}} = \frac{G \times \frac{4}{3}\pi R^{3}\rho}{R^{2}} = \frac{4}{3}\pi G\rho R\ \ \ ie,g \propto R$
For pendulum clock, $g$ will increase on the planet, so time period will decrease. But for spring clock, it will not change. Hence, $P$ will run faster than $S$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.