Timekeeping of Spring and Pendulum Clocks on Another Planet – Rankers Physics

Acceleration Due to Gravity and its variation: Practice Problem & Solution

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:
S will run faster than P
P will run faster than S
They will both run at the same rate as on the earth
None of these

Solution Explained:

To solve this problem, we apply the core principles of Acceleration Due to Gravity and its variation. Understanding the underlying formula is key to arriving at the correct answer below:

Since \(g \propto \rho R\), on a planet with twice the radius and same density, \(g' = 2g\). Pendulum time period decreases (\(T_p = 2\pi\sqrt{l/g}\)), so clock P ticks faster. Spring clock is unaffected.

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