JEE Main · 2020 · 09 Jan 2020 · Shift 2 · Gravitation

Planet

A

has mass

M

and radius

R

. Plant

B

has half the mass and half the radius of Planet

A

. If the escape velocities from the planets

A

and

B

are

V_{A}

and

V_{B}

, respectively, then

\frac{V _{A}}{V _{B}} = \frac{n}{4}

. The value of '

n

' is:

(A)2
(B)1
(C)4✓ Correct
(D)3

Answer: (C)

Solution

Escape speed is

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

. For planet B, with mass

\frac{M}{2}

and radius

\frac{R}{2}

, the ratio

\frac{M}{R}

is unchanged, so

V_{B} = \frac{2 G ( M /2 )}{R /2} = \frac{2 GM}{R} = V_{A}

. Hence

\frac{V _{A}}{V _{B}} = 1

, and matching this to

\frac{n}{4}

gives

n = 4

JEE Main · 2020 · 09 Jan 2020 · Shift 2 · Single correct option

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