Question

The pressure on square plate is measured by measuring the force on the plate and length of sides of plate. If the maximum error in the measurement of force and length are respectively $4$% and $2$%, the maximum error in measurement of pressure is..........

• A. 1%
• B. 2%
• C. 6%
• D. 8%

Answer 1

The correct option is D 8%

$\begin{array}{c}P=\text{Pressure}\\ f=\text{force}\\ A=\text{Area}\\ l=\text{length of}\\ \text{square.}\end{array}$

$\begin{array}{c}\text{Expression of}P=\frac{f}{A}\\ \therefore A=\mathrm{l\; X\; l}\\ P=\frac{f}{l^2}\end{array}$

$\begin{array}{c}\text{Taking log both side}\\ \log P=\log \left(\frac{f}{l^2}\right)\end{array}$

$\begin{array}{c}\log p=\log f-2\log l\\ \text{Partial differentiating both side}\\ \frac{\delta p}{p}=\frac{\delta f}{f}-2\frac{\delta l}{l}\end{array}$

$\text{Error is always added}$

$\%\text{error in}\frac{\delta P}{P}=\frac{\delta P}{P}\times 100\text{\%}$$=\frac{\delta f}{f}\times 100\%+2\frac{\delta l}{l}\times \left(100\text{\%}\right)$

$\frac{\delta P\times 100\%}{P}=$

$\begin{array}{cc}4\%+2\times \left(2\%\right)& \\ =4\%+4\%& =8\%\text{-Ans}\end{array}$