Block `A` is hanging from vertical spring of spring constant `K` and is rest. Block `B` strikes block `A` with velocity `v` and sticks to it. Then the value of `v` for which the spring just attains natural length is

Options

A. `sqrt((60mg^(2))/(k)`
B. `sqrt((6mg^(2))/(k)`
C. `sqrt((10mg^(2))/(k)`
D. `sqrt((mg^(2))/(k)`

Answer

B

Explanation

`x_(0) = (mg)/(k)`, after the collision speed of combined mass is `(V)/(2)`.
`(1)/(2) xx 2m((v^(2))/(2))+(1)/(2)k((mg)/(k))^(2) = 2 mg((mg)/(k))` so, `V = sqrt((6mg^(2))/(k))`