A spacecraft of mass $M$ moving with velocity $v$ in free space explodes and breaks into two pieces. After the explosion, a mass $m$ of the spacecraft is left stationary. The velocity of the other part is:

\frac{m v}{M - m}

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\frac{M + m}{M}

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\frac{M v}{M - m}

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\frac{M v}{m}

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Solution

The correct option is D $\frac{M v}{M - m}$
Let the velocity of the remaining part be $v_{f}$

Using law of conservation of momentum,
$M v = m \times 0 + (M - m) v_{f}$
$v_{f} = \frac{M v}{M - m}$

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A spacecraft of mass M moving with velocity v in free space explodes and breaks into two pieces. After the explosion, a mass m of the spacecraft is left stationary. The velocity of the other part is:

The correct option is D MvM−mLet the velocity of the remaining part be vfUsing law of conservation of momentum, Mv=m×0+(M−m)vfvf=MvM−m

A spacecraft of mass $M$ moving with velocity $v$ in free space explodes and breaks into two pieces. After the explosion, a mass $m$ of the spacecraft is left stationary. The velocity of the other part is:

The correct option is D $\frac{M v}{M - m}$
Let the velocity of the remaining part be $v_{f}$

Using law of conservation of momentum,
$M v = m \times 0 + (M - m) v_{f}$
$v_{f} = \frac{M v}{M - m}$