Question

A bullet of mass $10\text{g}$ leaves a rife at an initial velocity of $3000\text{m/s}$ and strikes the earth at the same level with a velocity of $2000\text{m/s}$. The work done in overcoming the resistance of air will be

• A. $2.5\times {10}^5\text{J}$
• B. $2.5\times {10}^4\text{J}$
• C. $2.5\times {10}^3\text{J}$
• D. $2.5\times {10}^2\text{J}$

Answer 1

The correct option is B $2.5\times {10}^4\text{J}$

Here, initial velocity of bullet $v_2=3000\text{m/s}$ and final velocity $v_1=2000\text{m/s}$
According to work energy theorem
Work done by resistance of air= Change in KE
The work done by resistance of air $=\frac{1}{2}m(v_1^2-v_2^2)$
$=\frac{1}{2}\times \frac{10}{1000}\left(\right(2000{)}^2-\left(3000{)}^2\right)$
$=-25000\text{J}$

The work done in overcoming the resistance of air will be equal to $25000\text{J}$