The spacecraft of mass $M$ moving with a velocity $v$ in free space explodes and breaks up into pieces. If after explosion a piece of mass $m$ comes to rest, the other pieces of spacecraft will have a velocity :

\frac{M v}{(M - m)}

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\frac{M v}{(M + m)}

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\frac{m v}{(M - m)}

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\frac{m v}{(M + m)}

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Solution

The correct option is A $\frac{M v}{(M - m)}$
Initial momentum $= M v$

Given at final situation $, m$ comes to rest.

So, final momentum $= (M - m) v_{1} ($ where , $v_{1}$ be velocity of $(M - m)$ part $)$

Since , there is no external force acting momentum is conserved.

$\Rightarrow$ (M-m) $v_{1}$ =Mv

$\Rightarrow v_{1} = \frac{M v}{(M - m)}$

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The spacecraft of mass M moving with a velocity v in free space explodes and breaks up into pieces. If after explosion a piece of mass m comes to rest, the other pieces of spacecraft will have a velocity :

The correct option is A Mv(M−m)Initial momentum=MvGiven at final situation,m comes to rest.So, final momentum=(M−m)v1(where ,v1 be velocity of (M−m) part)Since , there is no external force acting momentum is conserved.⇒(M-m)v1=Mv⇒v1=Mv(M−m)

The spacecraft of mass $M$ moving with a velocity $v$ in free space explodes and breaks up into pieces. If after explosion a piece of mass $m$ comes to rest, the other pieces of spacecraft will have a velocity :