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Question: 13. A bullet of mass \(m\) and velocity \(\alpha\) is fired into a large block of wood of mass \(M\)...

  1. A bullet of mass mm and velocity α\alpha is fired into a large block of wood of mass MM. What is the final velocity of the system if the bullet remains embedded in the block?
A

m+βMα\frac{m+\beta}{M} \alpha

B

Mm+αα\frac{M}{m+\alpha} \alpha

C

m+Mmα\frac{m+M}{m} \alpha

D

mm+Mα\frac{m}{m+M} \alpha

Answer

mm+Mα\frac{m}{m+M} \alpha

Explanation

Solution

From linear momentum conservation

ma=(M+m)vma = (M + m) v

or v=ma(M+m)v = \frac{ma}{(M + m)}