Question

The linear momentum of body is decreased by $20\%$. Then what is the $\%$ change in kinetic energy of the body.

• A. $20\%$ decreased
• B. $36\%$ decreased
• C. $40\%$ decreased
• D. $30\%$ decreased

Answer 1

The correct option is B $36\%$ decreased

Let, mass of the body be $m$
and the initial and final linear momentum are $P_1\text{and}{P}_2$
According to the question,
$P_2=80\%\text{of}{P}_1$
$P_2=\frac{8}{10}{P}_1$
$m{V}_2=\frac{8}{10}m{V}_1$
$V_2=\frac{8}{10}{V}_1$
Squaring both sides
$V_1^2=\frac{64}{100}{V}_1^2$
$\frac{1}{2}m{V}_2^2=\frac{64}{100}\left(\frac{1}{2}m{V}_1^2\right)$
$K_2=\frac{64}{100}{K}_1$
$\Delta K=K_1-K_2$
$\Delta K=K_1-\frac{64}{100}{K}_1=\frac{36}{100}{K}_1$
Thus kinetic energy of body is decreased by $36\%$