A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm , respectively. Using a

Question

A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm , respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be $\frac{x}{100}$ where $x$ is $\_\_\_\_$ .\

Professor PC Thomas Classes · Answer

(3) : Least count of the screw gauge $$ =\frac{	ext { Pitch }}{	ext { Number of divisions }} $$ $	herefore \quad$ Least count $=\frac{0.75}{15}=0.05 \mathrm{~mm}$\ Given that, length $L=5 \mathrm{~mm}$ and breath, $B =2.5 \mathrm{~mm}$\ Area of sheet can be calculated as, $A=L 	imes B$ For fractional error in the measurement of area, $$ \frac{d A}{A}=\frac{d L}{L}+\frac{d B}{B} $$ Here $d L=d B=0.05 \mathrm{~mm}$\ $	herefore \frac{d A}{A}=\frac{0.05}{5}+\frac{0.05}{2.5}=\frac{1}{100}+\frac{1}{50}=\frac{3}{100}$\ $	herefore x=3$