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Eight particles of mass 'm' each are pla...

Eight particles of mass 'm' each are placed at the verties of a cube of side 'a' . Find gravitational potential energy of this system . .

A

`-2(Gm^(2))/(a)(12+6sqrt(2)+(4)/(sqrt(3)))`

B

`-(Gm^(2))/(a)(12+6sqrt(2)+(4)/(sqrt(3)))`

C

`(Gm^(2))/(a)(12+6sqrt(2)+(4)/(sqrt(3)))`

D

`-(Gm^(2))/(2a)(12+6sqrt(2)+(4)/(sqrt(3)))`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
Total particles are `n = 8`
`:.` Total numbers of pairs are `n((n-1))/(2)` or `28`.
In `12` pairs , distance between the particles is 'a'. In `12`pairs , distance is `sqrt (2)a` and in remaining `4` pairs distance is `sqrt(3)a`.
`:. U = 12 ((-Gmm)/(a))+12 ((-Gmm)/(sqrt2a))+4((-Gmm)/(sqrt3a))`
`= -(Gm^(2))/(a)(12+6sqrt(2)+(4)/(sqrt(3)))`
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Knowledge Check

  • Four particles each of mass m are placed at the vertices of a square of side l. the potential at the centre of square is

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