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JEE Main 20209 JanuaryEvening Shift

Exam: JEE Main
Year: 2020
Date: 9 January
Shift: Evening Shift
Subject: Physics
Chapter: Gravitation

JEE Main 2020 · 9 January · Evening Shift · Physics · Gravitation

Planet A has mass M and radius R . Planet B has half the mass and...

Planet

A

has mass

M

and radius

R .

Planet

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

\dfrac{{v}_{A}}{{v}_{B}} = \dfrac{n}{4} .

The value of

n

is:

Options

A $4$
B $1$
C $2$
D $3$

Correct answer

A. $4$

Step-by-step solution

{v}_{e} = \sqrt{\dfrac{2GM}{R}}

∴ \dfrac{{v}_{A}}{{v}_{B}} = \dfrac{\sqrt{\dfrac{2GM}{R}}}{\sqrt{\dfrac{2GM / 2}{R / 2}}} = 1 = \dfrac{n}{4}

⇒ n = 4

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