Escape velocity of a body on a planet is $100 m s^{- 1}$ . What is the gravitational potential energy of the body at the surface, if the mass of the body is $1 k g$ ?

$- 5000 J$

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$- 1000 J$

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$- 2400 J$

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$5000 J$

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Solution

The correct option is A
$- 5000 J$

Given, escape velocity, $v_{e} = 100 m s^{- 1}$ , mass of the body, $m = 1 k g$
We know universal gravitational constant, $G = 6.67 \times 10^{- 11} N m^{2} k g^{- 2}$ .
Let $M$ be the mass of the planet and $R$ be the radius of the planet and $U$ be the gravitational potential energy.
We know, $v_{e} = \sqrt{\frac{2 G M}{R}} = 100$
$\Rightarrow 10000 = \frac{2 G M}{R} \Rightarrow \frac{G M}{R} = 5000$
Potential energy, $U = - \frac{G M m}{R} = 5000 \times 1 = - 5000 J$

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