A moving body of mass $2m$ and velocity $12 \mathrm{~m/s}$ collides with a body at rest of mass $4m$

Question

A moving body of mass $2m$ and velocity $12 \mathrm{~m/s}$ collides with a body at rest of mass $4m$ and sticks to it. Now the combined mass starts to move. What will be their combined velocity?

Professor PC Thomas Classes · Answer

(d) : Given initial mass $m_1 = 2m$ with velocity $u_1 = 12 \mathrm{~m/s}$, and target mass $m_2 = 4m$ at rest ($u_2 = 0$). After the collision, the bodies stick together, making the combined mass $M = 2m + 4m = 6m$. By the law of conservation of momentum: $m_1 u_1 + m_2 u_2 = M v \implies 2m(12) + 0 = 6mv \implies 24m = 6mv$. Solving for $v$, we get $v = 4 \mathrm{~m/s}$.