JEE Main · 2026 · 22 Jan 2026 · Shift 1 · Gravitation

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The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is ______ m/s.

(A)1000
(B) $2005$
(C) $10010$ ✓ Correct
(D) $10002$

Answer: (C)

Solution

Escape speed is

v_{e} = \frac{2 GM}{R} = \frac{2 G}{R} \cdot ρ \cdot \frac{4}{3} π R^{3} = R \frac{8 π Gρ}{3}

, so

v_{e} \propto R ρ

. With

R_{B} = 0.1 R_{A}

and

ρ_{B} = 0.1 ρ_{A}

\frac{v _{e B}}{v _{e A}} = 0.1 0.1 = \frac{1}{10 10}

. Hence

v_{e B} = \frac{10 \times 1 0 ^{3}}{10 10} = 10010 m/s

JEE Main · 2026 · 22 Jan 2026 · Shift 1 · Single correct option

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