First slide

Gravitaional potential energy

Question

A body is revolving very close to the surface of the planet. When mass of the planet suddenly reduced to half without any change in radius then

Moderate

A

Body falls on to the surface of the planet
B

Body escape from planet
C

Continue to move in the same orbit
D

it will move to an higher orbit

Solution

present orbital velocity is $\sqrt{\frac{G M}{R}}$ if mass of the planet becomes $\frac{M}{2}$ the orbital velocity suppose to be $\sqrt{\frac{G M}{2 R}}$ but the present velocity is $\sqrt{2}$ times more than this so it will escape as
$v_{e} = \sqrt{2} v_{o}$

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