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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=F/l². If the maximum errors in the measurement of force and length are 4% and 2% respectively, find the maximum percentage error in the pressure.

2

8

1

10

Solution:

P=F/l²
Taking logarithm on both sides,
logP = logF - 2logl
Differentiating,
ΔP/P = ΔF/F - 2Δl/l
Given that ΔF/F = 4% = 0.04 and Δl/l = 2% = 0.02
Therefore,
ΔP/P = 0.04 + 2 × 0.02 = 0.04 + 0.04 = 0.08 = 8%
Therefore, the maximum percentage error in the pressure is 8%.