Four particles, each of mass M, are equally spaced on a circle of radius R and move under their mutual gravitational attraction. The speed of each particle is:
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Question

Four particles, each of mass M, are equally spaced on a circle of radius R and move under their mutual gravitational attraction. The speed of each particle is:

G1 Physics · Accepted Answer

The four masses form a square on the circle. For one mass, the two adjacent masses are at distance √2R and the opposite one at 2R. The inward force is F = GM²/(√2R²) + GM²/(4R²). Setting F = Mv²/R givₑ v² = (GM/R)(2√2+1)/4, so v = (1/2)√[(GM/R)(1+2√2)]. Correct answer: B.