Gravitation

JEE Main level, single correct, medium

114 of 223

Question 114 of 223

The mass of the moon is 1144\dfrac{1}{144} times the mass of a planet and its diameter 116\dfrac{1}{16} times the diameter of a planet. If the escape velocity on the planet is v, the escape velocity on the moon will be:

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Answer: (A) v3\dfrac{v}{3}

As we know, escape velocity is given by, vescape=2GMR{v}_{escape}=\sqrt{\dfrac{2GM}{R}}
Now, vplanet=2GMR=v{v}_{planet}=\sqrt{\dfrac{2GM}{R}}=v
vMoon=2GM×16144×R=132GMR=v3{v}_{Moon}=\sqrt{\dfrac{2GM\times 16}{144\times R}}=\dfrac{1}{3}\sqrt{\dfrac{2GM}{R}}=\dfrac{v}{3}

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