Question

In a one dimensional collision of two particles, velocities are interchanged when:

(i) Collision is elastic and masses are equal

(ii) Collision is inelastic but masses are unequal

Select the correct alternative.

• A. only (i) is correct
• B. only (ii) is correct
• C. both (i) and (ii) are correct
• D. both (i) and (ii) are wrong

Answer 1

Answer: (A)

For elastic collision,
$v_{2}-v_{1}=u_{1}-u_{2}\ldots \ldots \left(\right.i\left.\right)$
Momentum conservation,
$m_{1}u_{1}+m_{2}u_{2}=m_{1}v_{1}+m_{2}u_{2}$
For equal masses,
$u_{1}+u_{2}=v_{1}+v_{2}\ldots \ldots \left(\right.ii\left.\right)$
Solving (i) & (ii) we get,
$v_{1}=u_{2}$ and $v_{2}=u_{1}$