Question

Three point masses , M each, are moving in a circle, each with a speed v, under their mutual gravitational attractive force. the distance between any two masses must be​

Answer 1

Given: Three point masses of M each, speed = v

To find: The distance between any two masses = ?

Solution:

• As we have not given the radius of the circle, so let the radius of the circle be R, as distance is d.

• We know that :

                 F = G x m1 x m2 / r²

• So, forces on each mass will be:

                 F = (2 x G x M² / d²) x cos30

                    = √3 x G x M² / d²

• Now, let the velocity be v

                 √3 x G x M² / d² = M x v² / R

• Now we know that, relation between radius of the circle and distance is:

                  2x d x sin (60°) / 3 = R

                  R = d / √3

• Now, putting value of R in the original equation, we get:

                 √3 x G x M² / d² = √3 x M x v² / d

                  d = G x M / v²

Answer:

                 The distance between any two masses is G x M / v².

Answer 2

Answer:

option d GM/V^2 is the answer. I hope the drawing helps in understanding better. All the best to you.

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