A planet in a distant solar system is $10$ times more massive than the earth and its radius is $10$ times smaller. Given that the escape velocity from the earth is $11 {k m s}^{- 1}$ , the escape velocity from the surface of the planet would be

1.1 k m / s

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11 k m / s

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110 k m / s

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0.11 k m / s

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Solution

The correct option is C $110 k m / s$
Escape velocity - Minimum velocity which is required to escape the body from earth's gravitational pull wherein it is independent of the mass and direction of projection of body.
$V_{e} = \sqrt{\frac{2 G M}{R}}$ = $11 k m / s$ for earth
Mass of the planet = $10M_e$
The radius of the planet= $\frac{R}{10}$
$V_{e} = \sqrt{\frac{2 G M \times 10}{\frac{R}{10}}}$
= $10 X 11 = 110 k m / s$

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