The percentage errors in measurements of mass and speed of a body are $2 \%$ and $3 \%$ respectively. What…
The percentage errors in measurements of mass and speed of a body are $2 \%$ and
$3 \%$ respectively. What is the percentage error in kinetic energy of the body?
$9 \%$
$5 \%$
$8 \%$
$0 \%$
Solution
Given percentage errors in mass and velocity $=2 \%$ and $3 \%$ respectively
The kinetic energy of the particle is given by
$\mathrm{KE}=\frac{\mathrm{mv}^{2}}{2}$
The percentage error in kinetic energy will be
$\frac{\Delta \mathrm{m}}{\mathrm{m}} \times 100+2 \frac{\Delta \mathrm{v}}{\mathrm{v}} \times 100$
$\begin{array}{l}
=2+6 \\
=8 \%
\end{array}$