Question

Two balls $A$ and $B$ having masses $1\text{kg}$ and $2\text{kg}$, moving with speeds $21\text{m/s}$ and $4\text{m/s}$ respectively in opposite direction, collide head on. After collision $A$ moves with a speed of $1\text{m/s}$ in the same direction, then :

• A. The velocity of $B$ after collision is $6\text{m/s}$ opposite to the direction before collision
• B. The coefficient of resitution is 0.2
• C. The loss of kinetic energy due to collision is $200\text{J}$
• D. The impulse of the force between the two balls is $40\text{N-s}$

Answer 1

Answer: (A), (B), (C)

The correct options are
A The velocity of $B$ after collision is $6\text{m/s}$ opposite to the direction before collision
B The coefficient of resitution is 0.2
C The loss of kinetic energy due to collision is $200\text{J}$



Momentum conservation gives
$21-8=1+2v\Rightarrow v=6\text{m/s}$
$e=\frac{6-1}{21+4}=\frac{1}{5}=0.2$
$\Delta K=\frac{1}{2}\frac{m_1{m}_2}{m_1+m_2}(v_1-v_2{)}^2(1-e^2)=200\text{J}$
$\Delta P=(21-1)=20\text{N-s}$
$\therefore$ (a), (b), (c)