Question

Two masses \(m_1\) and \(m_2\) moving with velocities \(V_1\) and \(V_2\) in opposite directions collide elastically and after collision \(m_1\) and \(m_2\) move with velocities \(V_2\) and \(V_1\) respectively. The ratio \(\frac{m_2}{m_1}\) is

• A. \(0.25\)
• B. \(0.50\)
• C. \(0.75\)
• D. \(1.0\)

Hint:

Exchange of velocities needs equal masses.

Answer 1

The Correct Option is D

Step 1: Use momentum:
Before: $m_1V_1+m_2V_2$ (with signs). After: $m_1V_2+m_2V_1$. Equate: $m_1(V_1-V_2)=m_2(V_1-V_2)$.

Step 2: Simplify:
Cancel the non-zero factor $V_1-V_2$: $m_1=m_2$.

Step 3: Energy check:
With equal masses, the energy $\tfrac12m(V_1^2+V_2^2)$ is unchanged after swapping. So it is elastic. Ratio $=1$, option (D).

Final Answer:
Momentum conservation alone gives m1 = m2. \[ \boxed{D} \]