Energy required to move a body of mass m from an orbit of radius 2 R to 3 R is [AIEEE 2002]

Correct Answer is : GMm6RG M m/6 R6RGMm

Correct Answer is : GMm6RG M m/6 R6RGMm

Test Index

Gravitation Part 1

Section: Physics

Question : 100 of 100

Marks: +1, -0

m

2 R

3 R

Solution:

Gravitational potential energy

E = -\frac{G M m}{r}

where

M=

mass of earth

m=

mass of body

r=

radius of earth

Energy required to move a body of mass

m

from an orbit of radius

2 R

3 R

=(

Potential energy of the Earth-mass system when mass is at distance

3 R)-

(Potential energy of the Earth-mass system when mass is at distance

2 R

)

= \frac{-G M m}{3 R} - \left( \frac{-G M m}{2 R} \right)

= \frac{-G M m}{3 R} + \frac{G M m}{2 R}

= \frac{-2 G M m + 3 G M m}{6 R} = \frac{G M m}{6 R}

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