Question

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

Answer 1

Answer: (B)

$g=\frac{4}{3}\pi \rho GR$ . If density is same than $g\propto R$ According to problem, ${{R}_{p}}=2{{R}_{e}}$ ${{g}_{p}}=2{{g}_{e}}$ For dock $P$ (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.