Question
A clock $S$ is based on oscillations 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 same density as earth but twice the radius then
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Answer
(b)
Time period of spring $=2 \pi \sqrt{\frac{k}{m}}$
Time period of pendulum $=2 \pi \sqrt{\frac{l}{g}}$
Time period of spring will not be affected by gravitational acceleration.
Let mass of earth be $m$
Mass of new planet $=\rho \times \frac{4}{3} \pi(2 R)^3=8 m$
$g_2=\frac{G M_2}{\left(R_2\right)^2}=\frac{G \times 8 M}{(2 R)^2}=2 g$
$T_2=2 \pi \sqrt{\frac{I}{2 g}}$
$T_2=\frac{T}{\sqrt{2}}$
Hence $P$ will move faster.
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