Question

Percentage error in the measurement of mass and speed are $2\%$ and $3\%$ respectively. The error in the estimation of kinetic energy obtained by measuring mass and speed will be

• A. $12\%$
• B. $10\%$
• C. $2\%$
• D. $8\%$

Answer 1

Answer: (D)

Percentage error in mass $=2 \%=\frac{2}{100}$ and
percentage error in speed $=3 \%=\frac{3}{100}$.
$K . E .=\frac{1}{2} m v^{2}$
Therefore the error in measurement of kinetic energy
$\frac{\Delta K . E .}{K . E .}=\frac{\Delta m}{m}+2 \times \frac{\Delta v}{v}$
$=\frac{2}{100}+2 \times \frac{3}{100}=\frac{8}{100}=8 \%$