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Conservation of Momentum

A spacecraft ...

Question

A spacecraft of mass $2000$ kg moving with a velocity of $600$ m/s suddenly explodes into two pieces. One piece of mass $500$ kg is left stationary. The velocity of the other part must be

600 m / s

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800 m / s

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1500 m / s

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1000 m / s

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Solution

The correct option is A $800 m / s$
Using momentum conservation,
$M U = m_{1} v_{1} + m_{2} v_{2}$
Here,
$M = 2000$ Kg, $U = 600$ m/s, $m_{1} = 500$ , $m_{2} = 1500$ , $u_{1} = 0$ m/s
Substituting these values $M U = m_{1} v_{1} + m_{2} v_{2}$ , we get,
$2000 \times 600 = 500 \times 0 + 1500 \times v_{2}$

$\Rightarrow v_{2} = \frac{2000 \times 600}{1500} = \frac{20 \times 200}{5} = 800$ m/s

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