A clock S is based on oscillation of a spring and a clock P is based on pendulum

Question

A clock S is based on oscillation 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

Options:

A . S will run faster than P

B . P will run faster than S

C . They will both run at the same rate as on the earth

D . None of these

Answer: Option B
:
B

g = \frac{4}{3} π ρ G R

. If density is same then

g \propto R

According to problem

R_{p} = 2 R_{e} ∴ g_{p} = 2 g_{e}

For clock P (based on pendulum motion)

T = 2 π \sqrt{\frac{l}{g}}

Time period decreases on planet so it will run faster because

g_{p} > g_{e}

For clock S (based on oscillation of spring)

T = 2 π \sqrt{\frac{m}{k}}

So it does not change.

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