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Thee uniform spheres each having a mass ...

Thee uniform spheres each having a mass M and raius a are kept in such a way that each touches the other two. Find the magnitude of the gravitational force on any of the spheres due to the other two.

Text Solution

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The correct Answer is:
A, B, C, D
`vecF_(CB)=(Gm^2)/(4a^2)cos60^0veci+(Gm^2)/(4a^2).sin60^0@vecj`
vecF_(CA)=-(Gm^2)/(4a^2) cos 60^@ veci+(Gm^2)/(4a^2).sin60^@vecj`.

`vecF_(CB)=vecF_(CB)+vecF_(CA)`
`=+vec(2Gm^2)/(4a^2) sin 60^@ vecj`
`=+(2Gm^2)/(4a^2)xxsqrt3/2`
Magnitude `=(sqrt3 Gm^2)/(4a^2)`
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