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 $\frac{v}{10}$ after being dropped from height $H$, then neglecting energy losses and taking $g=10\; ms^{-2}$ , the value of $H$ is close to :

Question

( A ) 0.2 km
( B ) 0.5 km
( C ) 0.4 km
( D ) 0.3 km