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A stationary shell explodes into two fragments having masses in the ratio 1: 2. The heavier fragment attains a kinetic energy of 100 joule. Find the kinetic energy released in the explosion in joules

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answer is 300.

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Detailed Solution

$Let mass of pieces are m_{1} = m and m_{2} = 2 m$

$Applying conservation of momentum,$

$m_{1} v_{1} = m_{2} v_{2}$

$\Rightarrow v_{1} = 2 v_{2}$

$Now,$

$\Rightarrow K E_{2} = \frac{1}{2} m_{2} v_{2}^{2} = 100$

$\Rightarrow K E_{2} = \frac{1}{2} \times 2 m \times {(\frac{v_{1}}{2})}^{2} = 100 J$

$\Rightarrow K E_{1} = \frac{1}{2} m_{1} v_{1}^{2} = 100 \times \frac{1}{2} \times 4 = 200 J$

$So, Total Kinetic Energy = 300 J$

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