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JEE Main 2008 (AIEEE) · Escape Velocity

Escape Velocity question from JEE Main 2008 (AIEEE)

Q75JEE Main 2008 · AIEEEEasy

Escape Velocity

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 $11\text{ km s}^{-1}$ $,$ the escape velocity from the surface of the planet would be

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Answer: (c)

$v_e = \sqrt{\frac{2GM}{R}} \propto \sqrt{M/R}$ .
$M' = 10M$ , $R' = R/10 \Rightarrow \frac{M'}{R'} = 100\frac{M}{R}$ .
$v_e' = \sqrt{100}\times 11 = 110\text{ km s}^{-1}$ .
So the answer is (c) $110\text{ km s}^{-1}$ .

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