Escape velocity of a body of $1 k g$ mass on a planet is $100 m / s$ . Gravitational potential energy of the body at the planet is:

- 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 $- 5000 J$
Escape velocity is given by formula

$v_{e} = \sqrt{\frac{2 G M}{R}}$

Now gravitational potential energy

$U_{G} = \frac{- G M m}{R}$

$U_{G} = - \frac{1}{2} m {v_{e}}^{2}$

$U_{G} = - \frac{1 \times 100^{2}}{2}$

$U_{G} = - 5000 J$

Thus gravitational potential energy of the planet is $- 5 k J$ .

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Escape velocity of a body of 1 kg mass on a planet is 100m/s. Gravitational potential energy of the body at the planet is:

The correct option is A −5000JEscape velocity is given by formula ve=√2GMR Now gravitational potential energy UG=−GMmR UG=−12mve2 UG=−1×10022 UG=−5000J Thus gravitational potential energy of the planet is −5kJ.

Escape velocity of a body of $1 k g$ mass on a planet is $100 m / s$ . Gravitational potential energy of the body at the planet is: