Question

A clock S is based on oscillations of a spring and a clock P is based on pendulum motion. Both clock 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 S
• C. they will both run at the same rates as on the earth
• D. they will both run at the equal rates, but not the same as on the earth

Answer 1

Answer: (B)

P will run faster than S

Frequency of first system $S$ is $\sqrt{k/m}$ where $k$ is the spring constant and $m$ is the mass of spring system.

Frequency of second system $P$ is $\sqrt{g/l}$ where $l$ is the length of the pendulum.

Now, Acceleration due to gravity is given as $g=GM/R^2=G\times \rho \times 4\pi R^3/3R^2=4\pi \rho GR/3$

As the $R$ is doubled, $g$ will get doubled, so the frequency of pendulum system $P$ will become $\sqrt{2}$ times of that of earth.

Thus now, $P$ will run faster than $S$.