A block of mass `m` collides with another block of mass `3m` completely inelastically as shown in figure. What is the maximum value of `v (` in `m//s)` for which the block `B` does not move. Assume that initially spring is in natural length and blocks `A` and `B` are at rest. `(K//m=100 S.I. `unit `)`

Answer

2

Explanation

Velocity of `(A+C)`,
`V_(1)=(V)/(1+3)=(V)/(4)`
If `B ` does not move, maximum compression`X` in the spring is
`(1)/(2) KX^(2)=(1)/(2)xx4m((v)/(4))^(2)`
`:. X=((4m)/(K)).(v)/(4)`
`:. KX=mu mg `
`rArr 100. sqrt((4)/(100)). (v)/(4)=1xx10`
`rArr v=2m//s` Ans. 2