Three solid spheres each of mass `m` and radius `R` are released from the position shown in Fig. What is the speed of any one sphere at the time of collision?

Explanation

Let `upsilon` be the velocity of each sphere at the time of collision Fig. Using law of conservation of mechanical energy, we have,
decrease in potential energy of the system = increase in kinetic energy of the system
or `3 (U_(f) - U_(i)) = 3 xx (1)/(2) m upsilon^(2)`
or `3((Gm xx m)/(2R) - (Gm xx m)/(d)) = 3 xx (1)/(2) m upsilon^(2)`
or `upsilon^(2) = Gm((1)/(R) -(2)/(d))` or `upsilon = sqrt(Gm ((1)/(R) - (2)/(d)))`