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  4. For a planet having mass equal to mass of the earth but radius is one fourth of radius of the earth. Then escape velocity for this planet will be

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Q. For a planet having mass equal to mass of the earth but radius is one fourth of radius of the earth.
Then escape velocity for this planet will be

AIPMTAIPMT 2000Gravitation

Solution:

$v_{e}=\sqrt{2 g R}=\sqrt{\frac{2 G M}{R}}$
If $R$ is $1 / 4$ th then $v_{e}=2 v_{e-\text { earth }}$
$=2 \times 11.2=22.4 \,km / \sec$.