A clock S is based on oscillation of a spring | vedclass

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Question

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 $

Vedclass · Accepted Answer

$P$ will run faster than $S$

Vedclass · Answer

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 $g=G M / R^{2}=G 	imes ho 	imes 4 \pi R^{3} / 3 R^{2}=$ $4 \pi ho G R / 3$

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 $S$.

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

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