Three blocks are placed on smooth horizontal surface and lie on same horizontal straight line. Block 1 and block 3 have mass `m` each and block 2 has mass `M (M gt gt m)`. Block 2 and block 3 are initially stationary, while block 1 is initially moving towards block 2 with speed `v` as shown. Assume that all collisions are head on and perfectly elastic. What value of `M//m` ensures that block 1 and block 3 have the same final speed?

Options

A. `5+sqrt(2)`
B. `5-sqrt(2)`
C. `2+sqrt(5)`
D. `3+sqrt(5)`

Answer

C

Explanation

Let `v_(1),v_(2) and v_(3)` velocities of blocks `1,2`, and `3` after suffering collision each.
`mv=mv_(1)+Mv_(2)` and `v_(1)-v_(2)=-v`
solving we get `v_(1)=(m-M)/(m+M)lt0`

`:.|v_(1)|=(M-m)/(m+M)`
and `v_(2)=(2m)/(m+M)xxv_(2)=(4Mmv)/((m+M)^(2))`
`:. (M-m)/(M+m)v=(4Mmv)/((M+m)^(2))`
`M^(2)-m^(2)=4Mmimplies M/m=2+sqrt(5)`