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Gravitation question

2023 · 13 Apr · Shift 2 · Q45
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Gravitation question

2023 · 13 Apr · Shift 2 · Q45

JEE MainPhysicsGravitationMCQ+4 / −1
Given below are two statements: Statement I : For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases. Statement II : Escape velocity is independent of the radius of the planet. In the light of above statements, choose the most appropriate answer form the options given below
  1. A
    Both Statement I and Statement II are correct
  2. B
    Statement I is correct but statement II is incorrect
  3. C
    Both Statement I and Statement II are incorrect
  4. D
    Statement I is incorrect but statement II is correct
View written solutionFree

Correct answer: B

  1. Formula for escape velocity

    The escape velocity from the surface of a planet is ve=2GMRv_e=\sqrt{\frac{2GM}{R}}ve​=R2GM​​ where:

    • GGG = gravitational constant
    • MMM = mass of the planet
    • RRR = radius of the planet

  2. Check Statement I

    Statement I says: If the ratio of mass of the planet to its radius increases, the escape velocity also increases.

    From the formula, ve∝MRv_e \propto \sqrt{\frac{M}{R}}ve​∝RM​​ So if MR\frac{M}{R}RM​ increases, then vev_eve​ increases.

    Therefore, Statement I is correct.

  3. Check Statement II

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

    But from ve=2GMRv_e=\sqrt{\frac{2GM}{R}}ve​=R2GM​​ we see that escape velocity depends on RRR.

    More precisely, ve∝1Rv_e \propto \frac{1}{\sqrt{R}}ve​∝R​1​ if MMM is kept constant.

    Therefore, Statement II is incorrect.

  4. Choose the correct option

    • Statement I: Correct
    • Statement II: Incorrect

    Hence, the correct option is: B\boxed{\text{B}}B​

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