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Standard XII

Physics

COM in Collision and Explosion

An explosion ...

Question

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 $m s^{- 1}$ and the second part of mass 2 kg moves with 8 $m s^{- 1}$ speed. If the third part files off with 4 $m s^{- 1}$ speed, then its mass is -

3 kg

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5 kg

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7 kg

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17 kg

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Solution

The correct option is B 5 kg
Just before and after the explosion Momentum of the system will be conserve.
From conservation of linear momentum:
$P_{i} = P_{f}$
$p_{1} + p_{2} + p_{3} = 0$

$∴ 1 \times 12 i + 2 \times 8 j + p_{3} = 0$
$12 i + 16^j + p_{3} = 0 ⟹ p_{3} = - (12 i + 16^j) | p_{3} | = \sqrt{(12)^{2} + (16)^{2}} = 20 k g - m / s p_{3} = m_{3} V_{3} m_{3} = \frac{p_{3}}{V_{3}} = \frac{20}{4} m_{3} = 5 k g$

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The correct option is B 5 kgJust before and after the explosion Momentum of the system will be conserve.From conservation of linear momentum:Pi=Pfp1+p2+p3=0∴1×12i+2×8j+p3=012i+16^j+p3=0⟹p3=−(12i+16^j)|p3|=√(12)2+(16)2=20kg−m/sp3=m3V3m3=p3V3=204m3=5kg