A bomb of mass 60 kg is at rest. It explodes | vedclass

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(D) The total mass of the bomb is $M = 60 \ kg$. It is at rest,so the initial momentum is $P_i = 0$.By the law of conservation of linear momentum,the

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$192$

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(D) The total mass of the bomb is $M = 60 \ kg$. It is at rest,so the initial momentum is $P_i = 0$.By the law of conservation of linear momentum,the final momentum must also be zero: $m_1 v_1 + m_2 v_2 = 0$,which implies $m_1 v_1 = -m_2 v_2$.Taking magnitudes,$p_1 = p_2 = p$.The kinetic energy $K$ is related to momentum $p$ by $K = \frac{p^2}{2m}$.Thus,$\frac{K_1}{K_2} = \frac{p^2 / 2m_1}{p^2 / 2m_2} = \frac{m_2}{m_1}$.Given $m_1 = 40 \ kg$ and $m_2 = 60 \ kg - 40 \ kg = 20 \ kg$.Given $K_1 = 96 \ J$.Substituting the values: $\frac{96}{K_2} = \frac{20}{40} = \frac{1}{2}$.Therefore,$K_2 = 96 	imes 2 = 192 \ J$.

$A$ bomb of mass $60 \ kg$ is at rest. It explodes into two fragments. The kinetic energy of the $40 \ kg$ fragment is $96 \ J$. What is the kinetic energy of the other fragment in $J$?

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