A bullet of mass ’m’ and velocity ’a’ is fired in to a large block of wood of mass ’M’. The final velocity of the system is

$frac{m+M}{m} a$

$frac{m}{m+M} a$

$frac{m+M}{M} a$

$frac{M}{m+M} a$

Answer : Option B

Explanation :

If v is the final velocity, then according to the principle of conservation of momentum

$mathrm{m}_{1} mathrm{v}_{1}+mathrm{m}_{2} mathrm{v}_{2}=left(mathrm{m}_{1}+mathrm{m}_{2} ight) mathrm{v}$ or, $mathrm{v}=mathrm{m}_{1} mathrm{v}_{1}+mathrm{m}_{2} mathrm{v}_{2} /left(mathrm{m}_{1}+mathrm{m}_{2} ight)$

Using values from the question, v = m a + 0/ (m + M) = ma/ (m + M)