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Question: A bullet of mass m and velocity a is fired into a large block of wood of mass M. The final velocity ...

A bullet of mass m and velocity a is fired into a large block of wood of mass M. The final velocity of the system is –

A

Mm+Ma\frac{M}{m + M}a

B

m+Mma\frac{m + M}{m}a

C

m+aMa\frac{m + a}{M}a

D

mm+Ma\frac{m}{m + M}a

Answer

mm+Ma\frac{m}{m + M}a

Explanation

Solution

From linear momentum conservation

ma = (M + m) v

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