Question

A body of mass $m_1$ is moving with a velocity $3m{s}^{-1}$ collides with another body at rest of mass $m_2$. After collision the velocities of the two bodies are $2m{s}^{-1}$ and $5m{s}^{-1}$ respectively along the direction of motion of $m_1$. The ratio $\frac{m_1}{m_2}$ is

• A. $\frac{5}{12}$
• B. $5$
• C. $\frac{1}{5}$
• D. $\frac{12}{5}$

Answer 1

The correct option is B $5$

Since there is no external force mmentum of system would remain conserved.

If target is at rest then final velocity of bodies are:

$v_1=\left(\frac{m_1-m_2}{m_1+m_2}\right)u_1.....\left(i\right)$

and $v_2=\frac{2m_1{u}_1}{m_1+m_2}.....\left(ii\right)$

From (i) and (ii)

$\frac{v_1}{v_2}=\frac{m_1-m_2}{2m_1}=\frac{2}{5}$

$\Rightarrow \frac{m_1}{m_2}=5$