Question

In the figure shown below, two particles have masses $2\text{kg}$ each and they are moving with velocities $4\text{m/s}$ and $2\text{m/s}$ respectively towards each other. Assume the collision between the particles is perfectly elastic. Find their respective magnitudes of velocities after the collision.

• A. $v_1=3\text{m/s};v_2=3\text{m/s}$
• B. $v_1=2\text{m/s};v_2=3\text{m/s}$
• C. $v_1=2\text{m/s};v_2=4\text{m/s}$
• D. $v_1=4\text{m/s};v_2=4\text{m/s}$

Answer 1

The correct option is C $v_1=2\text{m/s};v_2=4\text{m/s}$

Given,
$m_1=2\text{kg}$ ; $m_2=2\text{kg}$
$u_1=4\text{m/s}$ ; $u_2=-2\text{m/s}$
From principle of conservation of linear momentum:
$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$
$\Rightarrow v_1+v_2=2$ -------$\left(1\right)$
Since nature of collision is perfectly elastic, we get
$v_2-v_1=u_1-u_2$
$\Rightarrow v_2-v_1=6$ ---------$\left(2\right)$
From $\left(1\right)$ and $\left(2\right)$
$v_1=-2\text{m/s}$ and $v_2=4\text{m/s}$
(It means $m_1$ will move towards left and $m_2$ towards right after collision)