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(A) Given: Total mass $M = 12 \ kg$. Mass ratio $m_1:m_2 = 1:3$. Thus,$m_1 = 3 \ kg$ and $m_2 = 9 \ kg$. Since the bomb is initially at rest,the initi

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$36$

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(A) Given: Total mass $M = 12 \ kg$. Mass ratio $m_1:m_2 = 1:3$. Thus,$m_1 = 3 \ kg$ and $m_2 = 9 \ kg$. Since the bomb is initially at rest,the initial momentum is zero. By the law of conservation of momentum,the magnitudes of the momenta of the two fragments must be equal: $p_1 = p_2 = p$. The kinetic energy $K$ is related to momentum $p$ by $K = \frac{p^2}{2m}$,so $p = \sqrt{2mK}$. For the smaller fragment $(m_1 = 3 \ kg)$: $p = \sqrt{2 	imes 3 	imes 216} = \sqrt{1296} = 36 \ kg \cdot m/s$. Since the magnitudes of the momenta are equal,the momentum of the larger fragment is also $36 \ kg \cdot m/s$.

$A$ bomb of mass $12 \ kg$ initially at rest explodes into two fragments with a mass ratio of $1:3$. The kinetic energy of the smaller fragment is $216 \ J$. What is the momentum of the larger (heavier) fragment in $kg \cdot m/s$?

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