Question

The pitch of a screw gauge is 1 mm and there are 100 divisions on the circular scale. While measuring the diameter of a wire, the linear scale reads 1 mm and ${47}^{th}$ division on the circular scale coincides with the reference line. The length of the wire is 5.6 cm. Find the curved surface area (in $c{m}^2)$ of the wire in appropriate number of significant figures.

• A. $2.6$
• B. $3.2$
• C. $4.8$
• D. $1.3$

Answer 1

The correct option is A $2.6$

L.C. of the screw gauge $=\frac{Pitch}{Numberofdivisionsoncircularscale}=\frac{1}{100}=0.01mm$
Given : Main scale reading $=1mm$
Circular scale reading $=0.01\times 47=0.47$
$\therefore$ Diameter of wire $=$ Total reading $=1.47mm=0.147cm$
Curved surface area = $\pi \times dl=\pi \times \left(0.147\right)\left(5.6\right)=2.586\approx 2.6c{m}^2$