Question

A $1 \,kg$ ball moving with a speed of $6 \,ms ^{-1}$ collides head-on with a $0.5\, kg$ ball moving in the opposite direction with a speed of $9\, ms ^{-1}$. If the coefficient of restitution is $\frac{1}{3}$, then the energy lost in the collision is

• A. 303.4 J
• B. 66.7 J
• C. 33.3 J
• D. 67.8 J

Answer 1

Answer: (C)

Given, mass of first ball $\left(m_{1}\right)=1\, kg$
Speed of first ball $\left(u_{1}\right)=6 \,ms ^{-1}$
Mass of second ball $\left(m_{2}\right)=0.5 \,kg$ or $\frac{1}{2} \,kg$
Speed of second ball $\left(u_{2}\right)=9\, ms ^{-1}$
Coefficient of restitution $(e)=1 / 3$
We know that,
$\Delta KE =\frac{m_{1}\, m_{2}}{2\left(m_{1}+m_{2}\right)}\left(1-e^{2}\right)\left(u_{1}+u_{2}\right)^{2}$
$=\frac{1 \times \frac{1}{2}}{2\left(1+\frac{1}{2}\right)}\left[1-\left(\frac{1}{3}\right)^{2}\right](6+9)^{2}$
$=\frac{1}{2} \times \frac{2}{6} \times \frac{8}{9} \times(15)^{2}$
$=\frac{1}{6} \times \frac{8}{9} \times 225$
$=33.33 \,J $