Question

A bullet of mass $50\text{g}$ leaves a rifle at an initial velocity of $2000\text{m/s}$ and strikes the earth at the same level with a velocity of $1000\text{m/s}$. The work done in overcoming the resistance of air will be

• A. $750\text{J}$
• B. $7.5\times {10}^3\text{J}$
• C. $4500\text{J}$
• D. $7.5\times {10}^4\text{J}$

Answer 1

The correct option is D $7.5\times {10}^4\text{J}$

Given mass of the bullet, $m=50\text{g}$, initial velocity $v_1=2000\text{m/s}$ and final velocity $v_2=1000\text{m/s}$

By the work energy theorem,

Work done by resistive force ,
$W=$ Change in kinetic energy

$W=\frac{1}{2}\times m(v_2^2-v_1^2)$
as, $m=50\text{g}=\frac{50}{1000}\text{kg}$.

$W=\frac{1}{2}\times \left(\frac{50}{1000}\right)\times \left(\right(1000{)}^2-\left(2000{)}^2\right)$
$=-25\times 3000$
Work done by resistive force $=-75000\text{J}=-7.5\times {10}^4\text{J}$
Work has to be done to overcome this resistive force is$=7.5\times {10}^4\text{J}$

Hence option D is the correct answer.