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A shell of mass $20 \mathrm{~kg}$ at rest explodes into two fragments whose masses are in the ratio $2: 3$. The smaller fragment moves with a velocity of $6 \mathrm{~ms}^{-1}$. The kinetic energy of the larger fragment is
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$96 \mathrm{~J}$
Total mass of the shell $=20 \mathrm{~kg}$
Ratio of the masses of the fragments $=2: 3$
$\therefore$ Masses of the fragments are $8 \mathrm{~kg}$ and $12 \mathrm{~kg}$
Now, according to the conservation of momentum
$\quad m_{1} v_{1}=m_{2} v_{2}$ $\therefore \quad 8 \times 6=12 \times v$ $v($ velocity of the larger fragment) $=4 \mathrm{~m} / \mathrm{s}$ Kinetic energy $=\frac{1}{2} m v^{2}=\frac{1}{2} \times 12 \times(4)^{2}=96 \mathrm{~J}$
Kinetic energy $=\frac{1}{2} m v^{2}=\frac{1}{2} \times 12 \times(4)^{2}=96 \mathrm{~J}$
Ratio of the masses of the fragments $=2: 3$
$\therefore$ Masses of the fragments are $8 \mathrm{~kg}$ and $12 \mathrm{~kg}$
Now, according to the conservation of momentum
$\quad m_{1} v_{1}=m_{2} v_{2}$ $\therefore \quad 8 \times 6=12 \times v$ $v($ velocity of the larger fragment) $=4 \mathrm{~m} / \mathrm{s}$ Kinetic energy $=\frac{1}{2} m v^{2}=\frac{1}{2} \times 12 \times(4)^{2}=96 \mathrm{~J}$
Kinetic energy $=\frac{1}{2} m v^{2}=\frac{1}{2} \times 12 \times(4)^{2}=96 \mathrm{~J}$
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