A clock `S` is based on oscillations of a spring and clock `P` is based on pendulum motion, both clocks run at the same rate on Earth. On a planet having the same mass, but twice the radius that of the earth

Options

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

Answer

B

Explanation

Acceleration due to gravity,
`g = (GM)/(R^(2))=(Gxx(4)/(3)pi R^(3)rho)/(R^(2))=(4)/(3)pi G rho R`
or `g prop R`
For pendulum clock, g will increase on the plane, so time period will decrease. But for spring clock, it will not change. Hence, P will run faster than S.