Question

In one-dimensional collision of two particle velocities are interchanged when
$\left(i\right)$ collision is elastic and masses are equal
$\left(ii\right)$ collision is inelastic but masses are unequal
Select the correct alternative

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

Answer 1

The correct option is A

only $\left(i\right)$ is correct

Let the masses are unequal.
From the conservation of linear momentum,
$m_1{v}_1+m_2{v}_2=m_1{v}_2+m_2{v}_1$
$m_1(v_1-v_2)=m_2(v_1-v_2)$
$m_1=m_2$
i.e., mass of both the particles should be same.
$e=\frac{\text{relative velocity of separation}}{\text{relative velocity of approach}}$
$e=\frac{v_1-v_2}{v_1-v_2}=1$
$\Rightarrow$ collision is elastic.

Final answer: (a)