Two bodies $A$ and $B$ of the same mass undergo completely inelastic one-dimensional collision. The body $A$ m

Question

Two bodies $A$ and $B$ of the same mass undergo completely inelastic one-dimensional collision. The body $A$ moves with velocity $v_1$ while the body $B$ is at rest before collision. The velocity of the system after collision is $v_2$. The ratio of $v_1 : v_2$ is:

Accepted Answer

1. **Identify the System:** A completely inelastic collision occurs when two bodies stick together after impact and move with a common velocity. Momentum is conserved, but kinetic energy is not.
2. **Apply Conservation of Linear Momentum:**
   $$ m_A v_{1i} + m_B v_{2i} = (m_A + m_B)v_f $$
   Given: $m_A = m_B = m$, initial velocity of A is $v_1$, initial velocity of B is $0$, and final common velocity is $v_2$.
   $$ m(v_1) + m(0) = (m + m)v_2 $$
   $$ mv_1 = 2mv_2 $$
3. **Calculate Ratio:**
   $$ v_1 = 2v_2 $$
   $$ \frac{v_1}{v_2} = \frac{2}{1} $$ [Class 11 Physics, Ch 6, Sec 5.11]

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