If blocks collide elastically head - on , the ratio of maximum compression of the left spring and the right spring will be

Options

A. `3 : 5`
B. `2 : 3`
C. `5 : 4`
D. `5 : 2`

Answer

D

Explanation

`mv_(0) - 2 mv_(0) = mv_(1) + 2 mv_(2)` (i)
`v_(1) + v_(0) = v_(2) + (-v_(0))` (ii)
Solving `v_(1) = -(5v_(0))/(3) , v_(2) = (v_(0))/(3)`
Let the maximum compression be `x_(1)`
`(1)/(2) m ((5 v_(0))/(3))^(2) = (1)/(2) 2k x_(1)^(2) rArr x_(1)^(2) = ( 25 mv_(0)^(2))/(18 k)` (i)
Let the maximum compression be `x_(2)`
`(1)/(2) xx 2m ((v_(0))/(3))^(2) = (1)/(2) k x_(2)^(2) rArr x_(2)^(2) = ( 2mv_(0)^(2))/(9k)` (ii)
`(x_(1)^(2))/(x_(2)^(2)) = (25)/(4) rArr (x_(1))/(x_(2)) = (5)/(2)`