Question

A body of mass $m_1$ moving with certain velocity $V_0$ collides headon with another body of mass $m_2$ at rest. List-1 gives relation between $m_1$ and $m_2$ and List-2 gives velocity of $m_2$ after collision.

If e = 1,
Match List-1 with List -2

$\begin{array}{cccc}& \text{List-1}& & \text{List-2}\\ \text{(I)}& m_2=m_1& \text{(P)}& V_0\\ \text{(II)}& m_2=4m_1& \text{(Q)}& \frac{2V_0}{3}\\ \text{(III)}& m_2=2m_1& \text{(R)}& \frac{2V_0}{5}\\ \text{(IV)}& m_2=9m_1& \text{(S)}& \frac{4V_0}{9}\\ & & \text{(T)}& \frac{4V_0}{15}\\ & & \text{(U)}& \text{None}\end{array}$

• A. I $\to$ P, II $\to$ R, III $\to$ Q, IV $\to$ U
• B. I $\to$ P, II $\to$ Q, III $\to$ R, IV $\to$ U
• C. I $\to$ P, II $\to$ R, III $\to$ T, IV $\to$ Q
• D. I $\to$ P, II $\to$ R, III $\to$ S, IV $\to$ U

Answer 1

The correct option is A I $\to$ P, II $\to$ R, III $\to$ Q, IV $\to$ U


By COM $\Rightarrow m_1{V}_0=m_2{V}_2-m_1{V}_1\dots \dots \left(1\right)$

By e $\Rightarrow V_0=V_2+V_1\dots \dots \left(2\right)$

I) $V_2=V_0$

II) $\begin{array}{c}m{V}_0=4m{V}_2-m{V}_1\\ V_0=V_2+V_1\end{array}\}\Rightarrow 2V_0=5V_2\Rightarrow V_2=\frac{2V_0}{5}$

III) $\begin{array}{c}m{V}_0=2m{V}_2-m{V}_1\\ V_0=V_2+V_1\end{array}\}\Rightarrow 2V_0=3V_2\Rightarrow V_2=\frac{2V_0}{3}$

IV) $\begin{array}{c}m{V}_0=9m{V}_2-m{V}_1\\ V_0=V_2+V_1\end{array}\}\Rightarrow 2V_0=10V_2\Rightarrow V_2=\frac{V_0}{5}$