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JEE Main 2020 (9 Jan, Shift 2) · Escape Velocity

Escape Velocity question from JEE Main 2020 (9 Jan, Shift 2)

Q56JEE Main 2020 · 9 JAN · SHIFT 2Easy

Escape Velocity

Planet A has mass M and radius R. Planet B has half the mass and half the radius of Planet A. If the escape velocities from the Planets A and B are vA and vB, respectively, then $\frac{v_A}{v_B} = n$ $4$ . The value of n is:

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Answer: (c)

Escape speed $v = \sqrt{\frac{2GM}{R}}$ , so $v \propto \sqrt{M/R}$ .
Planet B: $\frac{M/2}{R/2} = \frac{M}{R}$ , same as planet A.
So $v_A = v_B$ , i.e. $\frac{v_A}{v_B} = 1 = \frac{n}{4}$ .
So the answer is (c) $n = 4$ .

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