Given below are two statements: one is labelled as Assertion A and… | JEE Main 2021 (25 Feb, Shift 1)

Q46JEE Main 2021 · 25 FEB · SHIFT 1Medium

Escape Velocity

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: The escape velocities of planet A and B are same. But A and B are of unequal mass. Reason R: The product of their mass and radius must be same. M1R1 = M2R2

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

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Answer: (c)

$v_e = \sqrt{\frac{2GM}{R}}$ , so equal $v_e$ needs equal $\frac{M}{R}$ , which is possible with unequal masses if radii differ in the same ratio. A is correct.
The condition is $\frac{M_1}{R_1} = \frac{M_2}{R_2}$ , not $M_1R_1 = M_2R_2$ . R is wrong.
So the answer is (c) A is correct but R is not correct.

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Escape Velocity question from JEE Main 2021 (25 Feb, Shift 1)

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