A block `A` of mass `m` is give a velocity `v_(0)` towards another block `B` of sae mass `B`. Is attached to an ideal spring of spring constant `K`. `A` makes a head on perfectly inelastic collision with `B`.
Answer the following two questions:
Q. Choose the correct option (s)

Options

A. Maximum elongation in the spring during subsequent motion is `(1)/(2)sqrt((mv_(0)^(2))/(K))`
B. Maximum elongation in the spring during subsequent motion is `sqrt((mv_(0)^(2))/(2K))`
C. Final velocity of block A is `(v_(0))/(2)`
D. Final velocity of block A is `(V_(0))/(4)`

Answer

A, C

Explanation

Max compression in spring
`(1)/(2)(2m)((v_(0))/(2))^(2)=(1)/(2)KX_(1)^(2)impliesX_(1)=sqrt((mv_(0)^(2)))/(2K))`
Max elongation in spring
`(1)/(2)m((v_(0))/(2))^(2)=(1)/(2)KX_(2)^(2)impliesX_(2)=(1)/(2)sqrt((mv_(0)^(2))/(K))`
B makes first half oscillation with A.
So, `t_(1)=pisqrt((2m)/(K))`
B makes rest half oscillation alone
`t_(2)=pisqrt((m)/(k))`
`t=t_(1)+t_(2)=pisqrt((m)/(K))(sqrt(2)+1)`