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(D) Initial kinetic energy of the system is $K_i = \frac{1}{2} m u^2$.By the law of conservation of linear momentum,the final velocity $v$ of the comb

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$80$

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(D) Initial kinetic energy of the system is $K_i = \frac{1}{2} m u^2$.By the law of conservation of linear momentum,the final velocity $v$ of the combined mass $(m + 4m = 5m)$ is given by:$m u + (4m)(0) = (5m) v$$m u = 5m v$$v = \frac{u}{5}$Final kinetic energy of the system is $K_f = \frac{1}{2} (5m) v^2 = \frac{1}{2} (5m) \left(\frac{u}{5}ight)^2 = \frac{1}{2} (5m) \frac{u^2}{25} = \frac{1}{10} m u^2$.The loss in kinetic energy is $\Delta K = K_i - K_f = \frac{1}{2} m u^2 - \frac{1}{10} m u^2 = \frac{5-1}{10} m u^2 = \frac{4}{10} m u^2 = \frac{2}{5} m u^2$.The percentage loss in kinetic energy is $\frac{\Delta K}{K_i} 	imes 100 = \frac{\frac{2}{5} m u^2}{\frac{1}{2} m u^2} 	imes 100 = \frac{4}{5} 	imes 100 = 80 \%$.

$A$ body of mass $m$ is moving with velocity $u$ as shown in the figure and it collides with a body of mass $4m$ at rest. If the collision is perfectly inelastic,then the percentage loss in kinetic energy is:

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