A force F is applied onto a square plate of side L. If the percentage error in determining L is 2% and that in F is 4%, the permissible percentage error in determining the pressure is

Answer (4)

Given,

$\displaystyle \frac {\Delta F} {F} \times 100=4\%, \frac {\Delta L} {L} \times 100=2\%$

Pressure, $P=\displaystyle \frac {F} {A}=\frac {F} {L^2}$

$\displaystyle\begin{aligned}\frac {\Delta P} {P} \times 100&=\frac {\Delta F} {F} \times 100+2\left(\frac {\Delta L} {L} \times 100\right)\\&=4+2\times 2=8\%\end{aligned}$