Question

A clock $S$ is based on osculation of a spring and a clock $P$ is based on pendulum motion. Both clocks 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 P
• 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

Answer 1

Answer: (B)

Acceleration due to gravity
$g =\frac{G M}{R^{2}}=\frac{G \times \frac{4}{3} \pi R^{3} \rho}{R^{2}} $
$=\frac{4}{3} \pi G \rho R $
or $g \propto R$
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 $S$.