3 uniform spheres each having a mass m and radius are kept in such a way that each touches the other

Asked by topperm | 28th Dec, 2009, 08:51: PM

Expert Answer:

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

TopperLearning

Answered by  | 29th Dec, 2009, 02:47: PM

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