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  4. Escape velocity of a 1 kg body on a planet is 100 m / s. The magnitude of potential energy (in joule) of the body at that planet is

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Q. Escape velocity of a $1 \,kg$ body on a planet is $100 \,m / s$. The magnitude of potential energy (in joule) of the body at that planet is

Gravitation

Solution:

$v_{\text {esc }}=\sqrt{\frac{2 G M}{R}}$
$100=\sqrt{\frac{2 G M}{R}}$
$ \Rightarrow \frac{G M}{R}=5000$
Gravtiational potential energy $=-\frac{G M m}{R} $
$=-5000 \times 1=-5000 \,J$