Three solid spheres each of mass m and radius R are released from the position shown in figure. The speed of any one sphere at the time of collision would be

Options

A. `sqrt(Gm(1/d-3/R))`
B. `sqrt(Gm(3/d-1/R))`
C. `sqrt(Gm(2/R-1/d))`
D. `sqrt(Gm(1/R-2/d))`

Answer

D

Explanation

From conservation of mechanical energy
`3{1/2mv^2}=3{(Gm^2)/(2R)-(Gm^2)/d}`
`rArr v^2=Gm{1/R-2/d} rArr v=sqrt(Gm{1/R-2/d})`