Two bodies $A$ and $B$ undergo a completely inelastic one-dimensional collision. Body $A$ has a mass

Question

Two bodies $A$ and $B$ undergo a completely inelastic one-dimensional collision. Body $A$ has a mass of $2m$ and moves with velocity $v_1$, while body $B$ has a mass of $3m$ and is initially at rest. The combined system moves with velocity $v_2$ after the collision. The ratio $v_1 : v_2$ is

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(b) : Given the masses $m_A = 2m$ and $m_B = 3m$, and initial velocities $u_A = v_1$ and $u_B = 0$. In a completely inelastic collision, the two bodies stick together and move with a common final velocity $v_2$. By the law of conservation of linear momentum: $m_A u_A + m_B u_B = (m_A + m_B)v_2$. Substituting the values: $(2m)v_1 + 0 = (2m + 3m)v_2 \implies 2mv_1 = 5mv_2$. Therefore, the ratio $v_1/v_2 = 5/2$.