Three objects `A` ,` B` and `C` are kept in a straight line on a smooth horizontal surface. These have masses `m `, `2m` and `3 m` , respectively . The head - on elastic collision takes place between `A` and `B` and then `B` makes completely inelastic collision with `C`. All motions occur on the same straight line. The final speed of `C` will be

Options

A. `(v_(0))/(15)`
B. `(2v_(0))/(15)`
C. `(3v_(0))/(15)`
D. `(4 v_(0))/(15)`

Answer

D

Explanation

The head - on elastic collision between `A` and `B`
`mv_(0) = mv_(1) + 2 mv_(2)` (i)
`v_(1) + v_(0) = v_(2) + 0` (ii)
Solving, `v_(2) = ( 2v_(0))/(3)`
Completely inelastic , the head - on collision between `B` and `C`
`2 m xx (2v_(0))/(3) = ( 2m + 3m) v rArr v = ( 4v_(0))/(15)`
Final speed of `C = ( 4v_(0))/(15)`