Assume there are two identical simple pendulum Clocks-1 is placed… - Vidyadip

MCQ

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 $....km$ (consider radius of earth $R _{ E }=6400\,km$ and $g$ on earth $10\,m / s ^{2}$ )

A
$1200$
B
$1600$
✓
$3200$
D
$4800$

✓

Answer

Correct option: C.

$3200$

c
$t \propto \frac{1}{\sqrt{ g }}$ and $g \propto \frac{1}{( R + h )^{2}}$

$\frac{t_{1}}{t_{2}}=\sqrt{\frac{g^{\prime}}{g}}=\sqrt{\frac{R^{2}}{(R+h)^{2}}}$

$\frac{ t _{1}}{ t _{2}}=\frac{4}{6}=\frac{ R }{( R + h )} \Rightarrow h =3200\,\,km$

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