Question

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

• A. $1\%$
• B. $2\%$
• C. $6\%$
• D. $8\%$

Answer 1

The correct option is D $8\%$

From formula
Pressure $\left(p\right)=\frac{F}{A}$
For square plate,
$p=\frac{F}{l^2}=F{l}^{-2}$
For maximum error in pressure measurement,
$\frac{\Delta p}{p}=\frac{\Delta F}{F}+\frac{2\Delta l}{l}$
$\Rightarrow \frac{\Delta p}{p}\times 100=(\frac{\Delta F}{F}\times 100)+2(\frac{\Delta l}{l}\times 100)$
$=4+(2\times 2)=8\%$
So $\%$ error in pressure is $8\%$.
Hence, option $\left(d\right)$ is the correct answer.