Escape velocity of a $1 kg$ body on a planet is $100 m/s$ . Potential energy of body at that planet is :

- 2400 J

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- 5000 J

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- 1000 J

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- 10000 J

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Solution

The correct option is B $- 5000 J$
$m = 1 kg$

$V_{e} = 100 m/sec$

Escape velocity is given by , $V_{e} = \sqrt{\frac{2 G M}{R}}$

Substituting the data we get,

$100 = \sqrt{\frac{2 G M}{R}}$

$\Rightarrow \frac{G M}{R} = 5000$

Now the potential energy is $U = - \frac{G M m}{R} = - 5000 \times 1 = - 5000 J$

Hence, option (a) is the correct answer.

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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 $1 k g$ ?

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Escape velocity of a 1 kg body on a planet is 100 m/s. Potential energy of body at that planet is :

The correct option is B −5000 Jm=1 kg Ve=100 m/sec Escape velocity is given by , Ve=√2GMR Substituting the data we get, 100=√2GMR ⇒GMR=5000 Now the potential energy is U=−GMmR=−5000×1=−5000 J Hence, option (a) is the correct answer.

Escape velocity of a $1 kg$ body on a planet is $100 m/s$ . Potential energy of body at that planet is :