Question

A $1kg$ ball moving with a speed of $6m{s}^{-1}$ collides head-on with a $0.5kg$ ball moving in the opposite direction with a speed of $9m{s}^{-1}$. 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 $\left(m_1\right)=1kg$
Speed of first ball $\left(u_1\right)=6m{s}^{-1}$
Mass of second ball $\left(m_2\right)=0.5kg$ or $\frac{1}{2}kg$
Speed of second ball $\left(u_2\right)=9m{s}^{-1}$
Coefficient of restitution $(e)=1/3$
We know that,
$\Delta KE=\frac{m_1{m}_2}{2\left(m_1+m_2\right)}\left(1-e^2\right){\left(u_1+u_2\right)}^2$
$=\frac{1\times \frac{1}{2}}{2\left(1+\frac{1}{2}\right)}\left[1-{\left(\frac{1}{3}\right)}^2\right](6+9{)}^2$
$=\frac{1}{2}\times \frac{2}{6}\times \frac{8}{9}\times (15{)}^2$
$=\frac{1}{6}\times \frac{8}{9}\times 225$
$=33.33J$