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
$g=\frac{GM}{R^2}=\frac{G\times \frac{4}{3}\pi R^3\rho }{R^2}$
$=\frac{4}{3}\pi G\rho R$
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 $S$.