CBSE Class 11-science Answered

Dear student,

Each of the spheres can be assumed to be point masses located at the center of each of the sphere of mass m. Hence the three spheres will constitute three particles each of mass m located at the vertices of an equilateral triangle of side 2r.

Force on each mass particle due to other sphere will be :

due to one sphere, F1 = Gm^2/(2r)^2

due to second sphere, F2 = Gm^2/(2r)^2

Note that F1 & F2 will be oriented along the two sides of the equilateral triangle at an angle of 60 deg.

So the resulatnt force on each sphere:

F'= sq rt. [F1^2+F2^2+2F1F2cos60]

On substituting,

F'=(sq rt.3)Gm^2/4r^2

Regards

Team

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