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 by using the formula $p=\frac{F}{l^2}$. If the maximum errors in the measurement of force and length are 4% and 2% respectively, then the maximum error in the measurement of pressure is :

• A. 1%
• B. 2%
• C. 8%
• D. 10%

Answer 1

Answer: (C)

8%

$P=\frac{F}{l^2}$

$⟹logP=logF-2logl$

$⟹\left|\frac{\Delta P}{P}\right|=\left|\frac{\Delta F}{F}\right|+\left|2\frac{\Delta l}{l}\right|$

$⟹\frac{\Delta P}{P}=0.04+2\times 0.02=0.08=8$%