Two blocks A and B of mass 2 m and m respectively are connected to a massless spring of spring constant K. if A and B moving on the horizontal frictionless surface with velocity v to right. If A collides with C of mass m elastically and head on, then the maximum compressions of the spring will be

Options

A. `sqrt((3)/(2)(m)/(k))V`
B. `sqrt((27m)/(8K))V`
C. `sqrt((9m)/(8K))V`
D. `sqrt((8m)/(27K))V`

Answer

D

Explanation

Velocity of a after the collision withh `C,V_(1)=(V)/(3)`
`therefore` velocity of each block A and B at maximum compression
`V_(2)=(5)/(9)V`
`therefore(1)/(2)kx^(2)+(1)/(2)3m((5)/(9)V)^(2)`
`=(1)/(2)mv^(2)+(1)/(2)2m((V)/(3))^(2)`
`x=sqrt((8m)/(27K))V`