In a screw gauge, there are 100 divisions on the circular scale and the main scale moves by 0.5 mm o

Question

In a screw gauge, there are 100 divisions on the circular scale and the main scale moves by 0.5 mm on a complete rotation of the circular scale. The zero of circular scale lies 6 divisions below the line of graduation when two studs are brought in contact with each other. When a wire is placed between the studs, 4 linear scale divisions are clearly visible while $46^{	ext {th }}$ division of the circular scale coincide with the reference line. The diameter of the wire is ________ $	imes 10^{-2} \mathrm{~mm}$.\

Professor PC Thomas Classes · Answer

(220) : LC of screw gauge\ $=\frac{0.5}{100}=\frac{1}{200} \mathrm{~mm}$\ Zero error $=\frac{+6}{200} \mathrm{~mm}$\ Main scale reading $=4 	imes 0.5$\ Therefore, width of wire $=4 	imes 0.5+\frac{16}{200}=2.23$\ Corrected width of wire $=2.23-0.03$ $$ \begin{aligned} & =2.20 \mathrm{~mm} \ & =220 	imes 10^{-2} \mathrm{~mm} \end{aligned} $$