A bullet of mass ‘m’ and velocity ‘a’ is fired in

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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

1. M a
  m + M
2. m a
  m + M
3. m + M a
  m
4. m + M a
  M

Correct Option: B

If v is the final velocity, then according to the principle of conservation of momentum,
m₁v₁ + m₂v₂ = (m₁+m₂)v;
or, v = m₁v₁ + m₂v₂/(m1+m2)
Using values from the question, v = m a + 0/ (m + M) = ma/ (m + M)