Gravitation

JEE Main level, single correct, medium

117 of 223

Question 117 of 223

Given below are two statements:
Statement I : For a planet, if the ratio of mass of the planet to its radius increase, the escape velocity from the planet also increase.

Statement II : Escape velocity is independent of the radius of the planet.

In the light of above statements, choose the most appropriate answer from the options given below

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Answer: (B) Statement I is correct but statement II is incorrect

The escape velocity is given by the formula
vesc=2GMR{v}_{\text{esc}}=\sqrt{\dfrac{2GM}{R}}
Clearly, the escape velocity depends on the mass and radius of the planet. Hence, if the ratio increases the escape velocity also increases.

So, Statement I is correct while statement II is wrong.

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