Question

If the percentage error in the measurement of momentum and mass of an object are $2 \%$ and $3 \%$ respectively, then maximum percentage error in the calculated value of its kinetic energy is

• A. $2 \%$
• B. $1 \%$
• C. $5 \%$
• D. $7 \%$

Answer 1

Answer: (D)

$KE =\frac{\text { Momentum }}{\text { Mass }}=\frac{p^{2}}{2 m}$
$\frac{\Delta K}{K} \times 100 \% =\left(\frac{2 \Delta p}{p} \times 100\right) \%+\left(\frac{\Delta m}{m} \times 100\right) \%$
$=2 \times 2 \%+3 \%$
$\frac{\Delta K}{K} \times 100 \% \Rightarrow 7 \%$