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Velocity of COM

A shell of ma...

Question

A shell of mass $20$ $k g$ at rest explodes into two fragments whose masses are in the ratio $2 : 3$ . The smaller fragment moves with a velocity of $6 m s^{- 1}$ . The kinetic energy of the larger fragment is:

96

J

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216

J

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144

J

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360

J

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Solution

The correct option is A $96$ $J$
From conservation of linear momentum,
$m_{1} v_{1} = m_{2} v_{2}$
$⟹ v_{2} = \frac{m_{1} v_{1}}{m_{2}} = \frac{m_{1}}{m_{2}} v_{1} = \frac{2}{3} \times 6 m / s$
$= 4 m / s$
Mass of the larger fragment: $m_{2} = \frac{3}{5} \times 20$ = $12 k g$
Thus, kinetic energy of the larger fragment = $\frac{1}{2} m_{2} v_{2}^{2}$
$= \frac{1}{2} (\frac{3}{5} \times 20) 4^{2} = 96 J$

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A shell of mass 20 kg at rest explodes into two fragments whose masses are in the ratio 2:3. The smaller fragment moves with a velocity of 6 ms−1. The kinetic energy of the larger fragment is:

The correct option is A 96 JFrom conservation of linear momentum,m1v1=m2v2⟹v2=m1v1m2=m1m2v1=23×6 m/s=4 m/sMass of the larger fragment: m2=35×20 = 12 kgThus, kinetic energy of the larger fragment = 12m2v22=12(35×20)42=96 J

A shell of mass $20$ $k g$ at rest explodes into two fragments whose masses are in the ratio $2 : 3$ . The smaller fragment moves with a velocity of $6 m s^{- 1}$ . The kinetic energy of the larger fragment is: