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There are three identical point mass bod...

There are three identical point mass bodies each of mass `m` locted at the vertices of an equilateral triangle with side `r`. They are experting gravitational force of attraction on each other, which can be given by Newton's law of gravitaiton. Each mass body produces its gravitational field in the surrounding region. the magnitude of gravitational field at a point due to a point mass body is the measure of gravitaitonal intensity at that point. The gravitational potential at a point in a gravitational field is the amount of workdone in bringing a unit mass body infinity to the given point without acceleration.

Answer the following questions :
Work done in taking one body far away from the other two bodies is

A

`-(Gm^(2))/(r )`

B

`(Gm^(2))/(r )`

C

`(2Gm^(2))/(r )`

D

`-(2Gm^(2))/(r )`

Text Solution

Verified by Experts

The correct Answer is:
C
When the three bodies are at the vertices of triangle `A, B` and `C`, then the gravitaitonal potential energy of the system is
`U_(1) = - (Gm xx m)/(r ) + ((-Gm^(2))/(r )) + ((-Gm^(2))/(r )) = - (3Gm^(2))/(r )`
When one body at `C` is taken for way from the other two bodies at `A` and `B`, there will be no interaction between bodies at far off distance with the bodies at `A` and `B`. Then the gravitaitonal potential energy of the system is
`U_(2) = - (Gm^(2))/(r )`
`:.` Work done in taking the body at `C` for away from the bodies
`= U_(2) - U_(1) = - (Gm^(2))/(r ) + (3Gm^(2))/(r ) = (2Gm^(2))/(r )`
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