From what minimum height `h`must the system be released when spring is unstretches so that after perfectly inelastic collision `(e =0)` with ground, `B` may be lifted off the gound: (Spring constant `=k)`

Options

A. `mg //(4k)`
B. `4mg//k`
C. `mg//(2k)`
D. None of the above

Answer

B

Explanation

Just after collision with ground, Applying `COE`
`(1)/(2)mv^(2) +mgx +(1)/(2) kx^(2) = (1)/(2)m (2gh) +0 +0`
`rArr (1)/(2) mv^(2) gt 0 rArr h gt 4mg//k`