Question

From what minimum height ${}^{\prime }{h}^{\prime }$ should the system be released when the spring is unstretched so that after a perfectly inelastic collision ($e=0$) with ground, ${}^{\prime }{B}^{\prime }$ may be lifted off the ground (spring constant $=k$)

• A. $\frac{mg}{2k}$
• B. $\frac{4mg}{k}$
• C. $\frac{mg}{4k}$
• D. $\frac{2mg}{k}$

Answer 1

The correct option is B $\frac{4mg}{k}$

$u=\sqrt{2gh}$
To lift block 'B' x (extesion in the spring) must be $\frac{2mg}{k}$

Using the energy conservation:
$0-\frac{1}{2}m{u}^2=-mgx-\frac{1}{2}k{x}^2$
$\frac{1}{2}m{u}^2=mg\left[\frac{2mg}{k}\right]+\frac{1}{2}k\frac{4m^2{g}^2}{k^2}$
$h=\frac{4mg}{k}$