A block of mass $m=10\;kg$ rests on a horizontal table. The coefficient of friction between the block and the table is $0.05$.When hit by a bullet of mass $50\; g$ moving with speed $v,$ that gets embedded in it, the block moves and comes to stop after moving a distance of $2\; m$ on the table. If a freely falling object were to acquire speed $\large\frac{v}{10}$ after being dropped from height H, then neglecting energy losses and taking $g=10 ms^{-2}$, the value of H is close to :

Question

$\begin{array}{1 1} 0.2\;km\\ 0.3\;km\\ 0.4\;km\\ 0.5\;km \end{array}$