JEE Main · 2023 · 13 Apr 2023 · Shift 2 · Gravitation

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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 from the options given below

(A)Both Statement I and Statement II are incorrect
(B)Statement I is correct but statement II is incorrect✓ Correct
(C)Statement I is incorrect but statement II is correct
(D)Both Statement I and Statement II are correct

Answer: (B)

Solution

Escape velocity is given by

v_{e} = \frac{2 GM}{R}

, which can be written as

v_{e} \propto \frac{M}{R}

. If the ratio

\frac{M}{R}

increases,

v_{e}

increases — so Statement I is correct. However,

v_{e} \propto \frac{1}{R}

shows that escape velocity depends on the radius, so Statement II is incorrect.

JEE Main · 2023 · 13 Apr 2023 · Shift 2 · Single correct option

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JEE Main · 2023 · 13 Apr 2023 · Shift 2 · Gravitation

Solution

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