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4 particles each of mass m and equidistant from each other move along a circle of radius R under the action of their mutual gravitation attraction the speed of each particle is

4 particles each of mass m and equidistant from each other move along a circle of radius R under the action of their mutual gravitation attraction the speed of each particle is

Grade:12th pass

1 Answers

Soumya Ranjan Mohanty
117 Points
6 years ago
Dear student,
We know formula for gravitational force between any 2 masses is Gm1m2/d^2
here if we draw the diagram, F31= Gm1m2/d^2=Gm^2/(4r^2)
F21=Gm^2/(sqrt(2)r)^2
F41=F21
resultant of F21 and F21=sqrt(Gm^2/(2r^2) + Gm^2/(2r^2))
=sqrt(2)Gm^2/r^2
so Fnet=F31+resultant of F21 and F21
=Gm^2/r^2 *(1/4 +sqrt(2))
we also know that gravitational force=mv^2 /r here
so Gm^2/r^2 *(1/4 +sqrt(2))=mv^2 /r
so v=1/2 sqrt(Gm(1+4sqrt(2))/r) [Ans]
Regards,
Thank You,
Soumya Ranjan Mohanty.

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