Question

A metal ball of mass $2\text{kg}$ moving with speed of $36\text{kmph}$ is having a collision with a stationary ball of mass $2\text{kg}$. If after collision, both the balls move together, the loss in kinetic energy due to collision is:

• A. $80\text{J}$
• B. $40\text{J}$
• C. $60\text{J}$
• D. $160\text{J}$

Answer 1

The correct option is C $60\text{J}$

Let $v$ be the common velocity.
Applying conservation of momentum
$2\times 10+3\times 0=(2+3)v$
$v=\frac{10\times 2}{5}=4\text{m/sec}$
[36 km/hour = 10 m /sec]
Initial Energy $=\frac{1}{2}\times 2\times (10{)}^2+0=100J$
Final Energy $=\frac{1}{2}\times 5\times 4\times 4=40J$
Loss of energy $=100-40=60\text{J}$