JEE Main · 2021 · 16 Mar 2021 · Shift 2 · Gravitation

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If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs so be supplied will be

\frac{x}{5} \frac{G M ^{2}}{R}

where

x

is ⋯----. (Round off to the Nearest Integer)
(

M

is the mass of earth,

R

is the radius of earth,

G

is the gravitational constant)

Answer: 3

Solution

Assembling a uniform sphere of mass

M

and radius

R

out of matter brought in from infinity releases an amount of energy equal to the magnitude of its gravitational self-energy,

U = - \frac{3}{5} \frac{G M ^{2}}{R}

Breaking the planet up completely means carrying every element of its mass back out to infinity, which costs exactly that amount:

E = \frac{3}{5} \frac{G M ^{2}}{R}

Comparing this with

\frac{x}{5} \frac{G M ^{2}}{R}

gives

x = 3

JEE Main · 2021 · 16 Mar 2021 · Shift 2 · Integer answer

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