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Two particles of equal mass m move in a circle of radius r under the action of their mutual gravitational attraction. The speed of each particle will be :Gm2r−−−√4Gmr−−−−√Gmr−−−√Gm4r−−−√

Question

Two particles of equal mass m move in a circle of radius r under the action of their mutual gravitational attraction. The speed of each particle will be :Gm2r−−−√4Gmr−−−−√Gmr−−−√Gm4r−−−√

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Solution

The force of gravitational attraction between the two particles is given by:

F = Gm^2/r^2

This force provides the centripetal force for the circular motion of the particles. The centripetal force is given by:

F = mv^2/r

Setting these two equations equal to each other gives:

Gm^2/r^2 = mv^2/r

Solving for v (the speed of each particle) gives:

v = sqrt(Gm/r)

So, the speed of each particle is the square root of the gravitational constant times the mass of the particles divided by the radius of the circle.

This problem has been solved

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