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)) - (G xx (4)/(3) pi R^(3) rho)/(R^(2)) = (4)/(3) pi G rho R or g prop R`
For pedulum 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.