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Three solid spheres each of mass m and radius R are placed at three corners of an equilateral triangle of side ‘d’ released. The speed of any one sphere at the time of collision would be d>2R [Assume there is no external gravitational force acting on the system of three spheres].

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a

Gm1d−3R

b

Gm3d−1R

c

Gm2R−1d

d

Gm1R−2d

answer is D.

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Detailed Solution

From conservation of mechanical energy Energy of system at the instance of release = Energy of system at the instance of Collision∴ 3−Gm2d=3−Gm22R+312mv2 and v=Gm1R−2dTherefore, the correct answer is (D).

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Three solid spheres each of mass m and radius R are placed at three corners of an equilateral triangle of side ‘d’ released. The speed of any one sphere at the time of collision would be d>2R [Assume there is no external gravitational force acting on the system of three spheres].