Question

Two balls of masses $2\text{kg}$ and $5\text{kg}$ moving on a frictionless surface, collide head-on with speeds $2\text{m/s}$ and $3\text{m/s}$ as shown in figure. If the coefficient of restitution is $0.25$, then the kinetic energy lost by the balls is

• A. $0.65\text{J}$
• B. $0.35\text{J}$
• C. $0\text{J}$
• D. $16.74\text{J}$

Answer 1

The correct option is D $16.74\text{J}$

Given,
$m_1=2\text{kg};m_2=5\text{kg}$
$u_1=2\text{m/s};u_2=3\text{m/s}$ and $e=0.25$

Loss in kinetic energy
$=\frac{1}{2}\left(\frac{m_1{m}_2}{m_1+m_2}\right)(u_1-u_2{)}^2(1-e^2)$
$=\frac{1}{2}\times \left(\frac{2\times 5}{2+5}\right)(2+3{)}^2(1-\frac{1}{16})$
$=\frac{1}{2}\times \frac{10}{7}\times 25\times \left(\frac{15}{16}\right)$
$=16.74\text{J}$