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(B) Since the particle is initially stationary,the initial momentum is $0$.By the law of conservation of linear momentum,the final momentum must also

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$m_A : m_B$

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(B) Since the particle is initially stationary,the initial momentum is $0$.By the law of conservation of linear momentum,the final momentum must also be $0$.Therefore,the magnitudes of the momenta of the two parts must be equal: $|P_A| = |P_B|$,which implies $m_A v_A = m_B v_B$.The kinetic energy of a particle is given by $K = \frac{P^2}{2m}$.Thus,the ratio of kinetic energies is $\frac{K_B}{K_A} = \frac{P_B^2 / 2m_B}{P_A^2 / 2m_A}$.Since $|P_A| = |P_B|$,this simplifies to $\frac{K_B}{K_A} = \frac{2m_A}{2m_B} = \frac{m_A}{m_B}$.

$A$ stationary particle breaks into two parts of masses $m_A$ and $m_B$ which move with velocities $v_A$ and $v_B$ respectively. The ratio of their kinetic energies $(K_B : K_A)$ is

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