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Question

# The spacecraft of mass M moves with velocity V in free space at first, then it explodes breaking into two pieces. If after explosion a piece of mass m comes to rest, the other piece of spacecraft will have a velocity:

A
MV(Mm)
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B
MV(M+m)
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C
mV(Mm)
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D
mV(M+m)
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Solution

## The correct option is A MV(M−m)Initial momentum of the system Pi=MVLet the mass of one part be mIts velocity V=0So, mass of other part m′=M−mLet its velocity be V′.Final momentum of the system Pf=mV+m′V′Or Pf=0+(M−m)V′=(M−m)V′Applying the conservation of linear momentum Pf=Pi∴ (M−m)V′=MV⟹ V′=MVM−m

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