JEE Main · 2024 · 30 Jan 2024 · Shift 2 · Gravitation

Escape velocity of a body from earth is

11.2 km / s

. If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the plate is:

(A) $11.2 km / s$
(B) $8.4 km / s$
(C) $4.2 km / s$
(D) $7.9 km / s$ ✓ Correct

Answer: (D)

Solution

Escape velocity from a body of mass

M

and radius

R

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

For the planet,

R_{P} = \frac{R _{E}}{3}

and

M_{P} = \frac{M _{E}}{6}

. Taking the ratio:

\frac{v _{P}}{v _{E}} = \frac{M _{P}}{M _{E}} \times \frac{R _{E}}{R _{P}} = \frac{1}{6} \times 3 = \frac{1}{2} = \frac{1}{2}

v_{P} = \frac{11.2}{2} \approx 7.9 km/s

JEE Main · 2024 · 30 Jan 2024 · Shift 2 · Single correct option

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