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 a

Question

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 $10 m s^{- 2}$ )

TestHub · Accepted Answer

The time period of a simple pendulum is given by, $T = 2 π \sqrt{\frac{l}{g}}$ .
Therefore, $T \propto \frac{1}{\sqrt{g}}$ .
The acceleration due to gravity at height $h$ from the surface of the earth is given by, $g^{'} = \frac{g}{{(R + h)}^{2}}$
Therefore,
$\frac{T_{1}}{T_{2}} = \sqrt{\frac{g_{2}}{g_{1}}} \Rightarrow \frac{4}{6} = \frac{R}{R + h} \Rightarrow h = \frac{R}{2} = 3200 km$

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