Q80 / 90 · JEE Main 2023 (13 Apr Shift 2) · Physics

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

  • A
    Statement I is incorrect but Statement II is correct
  • Correct answer
    B
    Statement I is correct but statement II is incorrect
  • C
    Both Statement I and Statement II are incorrect
  • D
    Both Statement I and Statement II are correct

Solution

The escape velocity is given by the formula

vesc =2GMR

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.

Hence, the correct answer is option: 'B'.

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