Question

A force $F$ is applied on a square plate of length $L$. If the percentage error in the determination of $L$ is $3\%$ and in $F$ is $4\%$, the permissible error in the calculation of pressure is

• A. 13%
• B. 10%
• C. 7%
• D. 12%

Answer 1

Answer: (B)

Given,
Percentage error in length $=3\%$
Percentage error in force $=4\%$
We know that,
Pressure, $P=\frac{F}{A}$
Area of square $=(L{)}^2$
$P=\frac{F}{L^2}$
$\frac{\Delta P}{P}=\frac{\Delta F}{F}+\frac{2\Delta L}{L}$
$\left(\frac{\Delta P}{P}\times 100\right)=\left(\frac{\Delta F}{F}\times 100\right)+2\left(\frac{\Delta L}{L}\times 100\right)$
$=4\%+2(3\%)=10\%$