Physics

Problem

The side of a square aluminium plate is measured to be

s = 12.4\,\text{cm} \pm 0.1\,\text{cm}

. The plate is used as a reference area in a laboratory experiment. (a) Calculate the area

A

of the plate. (b) Determine the absolute uncertainty in the calculated value of

A

. (c) Express the final value of the area with its uncertainty using the correct number of significant figures.

Intuitive explanation

This problem is about propagating measurement uncertainty through a calculation. When you square a measured length that has uncertainty, that uncertainty grows—you need to figure out by how much. The key insight is that small errors in the input ( $s$ ) become amplified in the output ( $A = s^2$ ), so you'll use the derivative to relate fractional uncertainties: a small relative error in $s$ gets doubled in $A$ .

Intuitive explanation

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