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  4. Assume there are two identical simple pendulum Clocks- 1 is placed on the earth and Clock-2 is placed on a space station located at a height h above the earth surface. Clock-1 and Clock- 2 operate at time periods 4 s and 6 s respectively. Then the value of h is (consider radius of earth RE=6400 km and g on earth 10 m / s 2 )

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Q. Assume there are two identical simple pendulum Clocks- 1 is placed on the earth and Clock-2 is placed on a space station located at a height $h$ above the earth surface. Clock-1 and Clock- 2 operate at time periods $4 s$ and $6 s$ respectively. Then the value of $h$ is (consider radius of earth $R_E=6400\, km$ and $g$ on earth $10 \, m / s ^2$ )

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Solution:

$t \propto \frac{1}{\sqrt{g}} \text { and } g \propto \frac{1}{( R + h )^2} $
$\frac{t_1}{t_2}=\sqrt{\frac{g^{\prime}}{g}}=\sqrt{\frac{R^2}{(R+h)^2}}$
$\frac{t_1}{t_2}=\frac{4}{6}=\frac{R}{(R+h)}$
$ \Rightarrow h=3200\, km $