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

• 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 1

The correct option is B P will run faster than S

$g=\frac{4}{3}\pi \rho GR$. If density is same then $g\propto R$ According to problem $R_p=2R_e\therefore g_p=2g_e$
For clock P (based on pendulum motion) $T=2\pi \sqrt{\frac{l}{g}}$
Time period decreases on planet so it will run faster because $g_p>g_e$
For clock S (based on oscillation of spring) $T=2\pi \sqrt{\frac{m}{k}}$
So it does not change.