Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 $\mathrm{km} / \mathrm{s}$, the escape velocity in km/s from the planet will be :

JEE Main · 2025 · 28 Jan 2025 · Shift 2 · Gravitation

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2

km / s

, the escape velocity in km/s from the planet will be :

(A)11.2
(B)5.6✓ Correct
(C)2.8
(D)8.4

Answer: (B)

Solution

The escape velocity from a spherical body of mass

M

and radius

R

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

For the planet compared to Earth:

\frac{( v _{esc} ) _{P}}{( v _{esc} ) _{E}} = \frac{M _{P}}{M _{E}} \times \frac{R _{E}}{R _{P}}

Given

M_{E} = 8 M_{P}

and

R_{E} = 2 R_{P}

\frac{( v _{esc} ) _{P}}{( v _{esc} ) _{E}} = \frac{1}{8} \times 2 = \frac{1}{4} = \frac{1}{2}

(v_{esc})_{P} = \frac{1}{2} \times 11.2 = 5.6 km/s

JEE Main · 2025 · 28 Jan 2025 · Shift 2 · Single correct option

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