Question

The minimum height h,through which the system be released from rest and the spring is unstretched initially,is $\frac{xmg}{k}$ .And collision between block B and surface is perfectly inelastic,such as after collision between B and ground 'B' may be lifted off from the ground after collision then x is:
(spring constant=k)

Answer 1

$u=\sqrt{2gh}$
to lift block 'B' x (extesion in the spring)must be
$\frac{2mg}{k}$
$0-\frac{1}{2}m{u}^2=-mgx-\frac{1}{2}k{x}^2$
$\frac{1}{2}m{u}^2=mg\left(\frac{2mg}{k}\right)+\frac{1}{2}k\frac{4m^2{g}^2}{k^2}$
$h=\frac{4mg}{k}$