Question

Two particles $A$ and $B$ of masses $10kg$ and $38kg$ respectively are moving along the same straight line with velocities $15m/s$ and $3m/s$ respectively in the same direction. After elastic collision the velocities of $A$ and $B$ are $v_A$ and $v_B$ in the direction of initial motion. Then:

• A.
  $v_A=-4,v_B=8$
• B.
  $v_A=20,v_B=8$
• C.
  $v_A=16,v_B=28$
• D.
  $v_A=-5,v_B=10$

Answer 1

The correct option is A

$v_A=-4,v_B=8$
In elastic collision the coefficient of restitution $e=1$
In the given problem, the velocity of $A$ can be calculated as
$v_A=\left(\frac{m_1-m_2}{m_1+m_2}\right)u_1+\frac{2m_2{u}_2}{m_1+m_2}$
Here, $m_1=10kg,m_2=38kg,u_1=15m/s,u_2=3m/s$
$=\left(\frac{10-38}{10+38}\right)15+\frac{2\times 30\times 3}{10+38}=-4m/s$
And the velocity of $B$ can be calculated as
$v_B=\left(\frac{m_2-m_1}{m_1+m_2}\right)u_2+\frac{2m_1{u}_1}{m_1+m_2}$
$=\left(\frac{38-10}{10+38}\right)3+\frac{2\times 10\times 15}{10+38}=8m/s$

Final answer: (b)