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−−−√
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.
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