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JEE Main 202622 JanuaryMorning Shift

Exam: JEE Main
Year: 2026
Date: 22 January
Shift: Morning Shift
Subject: Physics
Chapter: Gravitation

JEE Main 2026 · 22 January · Morning Shift · Physics · Gravitation

The escape velocity from a spherical planet A is 10 ~km / s . The...

The escape velocity from a spherical planet

A

is

10 \mathrm{~km} / \mathrm{s}

. The escape velocity from another planet

B

whose density and radius are

10 \%

of those of planet

A

, is

\_\_\_\_

\mathrm{m} / \mathrm{s}

.

Options

A1000
B $1000 \sqrt{2}$
C $200 \sqrt{5}$
D $100 \sqrt{10}$

Correct answer

D. $100 \sqrt{10}$

Step-by-step solution

Escape velocity

v_e = R\sqrt{\frac{8\pi G\rho}{3}} \propto R\sqrt{\rho}

.
Planet B:

\rho_B = 0.1\rho_A

,

R_B = 0.1R_A

.

\frac{v_B}{v_A} = \frac{0.1R_A\sqrt{0.1\rho_A}}{R_A\sqrt{\rho_A}} = 0.1\sqrt{0.1} = \frac{1}{10\sqrt{10}}

.

v_B = 10 \times \frac{1}{10\sqrt{10}} = \frac{1}{\sqrt{10}}

km/s

= \frac{1000}{\sqrt{10}} = 100\sqrt{10}

m/s.

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