A clock S is based on oscillation of a spring and a clock P is based on pendulum motion. Both clocks

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7.Gravitation

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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

Solution

(b) $g = \frac{4}{3}\pi \rho GR$. If density is same then $g \propto R$

According to problem ${R_p} = 2{R_e}$ $\therefore$ ${g_p} = 2{g_e}$

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.

Standard 11

Physics

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