In the figure shown, the two identical balls of mass `M` and radius `R` each, are placed in contact with each other on the frictionless horizontal surface. The third ball of mass `M` and radius `R//2`, is coming down vertically and has a velocity `= v_(0)` when it simultaneously hits the two balls and itself comes to rest. Then, each of the two bigger balls will move after collision with a speed equal to

Options

A. `4v_(0)//sqrt(5)`
B. `2v_(0)//sqrt(5)`
C. `v_(0)//sqrt(5)`
D. none of these

Answer

C

Explanation

`Jcostheta=Mv` ………..i
` -Jsintheta=0-Mv_(0)`
`Jsintheta=Mv_(0)`………ii
from eqn i and ii `tantheta=v_(0)/v` ………..iii

From `/_\AOC`
`tantheta=(sqrt5R/2)/(R/2)=sqrt(5)`
`sqrt(5)=v_(0)/vimpliesv=v_(0)/sqrt(5)`