Question

The velocity of a body increases by $10\%$. The percentage increase in its kinetic energy is

• A. $10\%$
• B. $21\%$
• C. $40\%$
• D. $38\%$

Answer 1

Answer: (B)

Here, $v^{\prime }=v+\frac{10}{100}v=\frac{11}{10}v$
$\therefore \frac{k^{\prime }}{k}=\frac{\frac{1}{2}m{v}^{\prime 2}}{\frac{1}{2}m{v}^2}$ or $\frac{k^{\prime }}{k}={\left(\frac{v^{\prime }}{v}\right)}^2={\left(\frac{11}{10}\right)}^2$
Now, $\%$ increase in kinetic energy
$=\left(\frac{k^{\prime }-k}{k}\right)\times 100$
$=\left(\frac{k^{\prime }}{k}-1\right)\times 100$
$=\left(\frac{121}{100}-1\right)\times 100$
$=21\%$