Question

A screw gauge of pitch $0.5mm$ is used to measure the diameter of uniform wire of length $6.8cm$, the main scale reading is $1.5mm$ and circular scale reading is $7$. The calculated curved surface area of wire to appropriate significant figures is :
[Screw gauge has $50$ divisions on its circular scale]

• A. $3.9c{m}^2$
• B. $2.4c{m}^2$
• C. $3.4c{m}^2$
• D. $6.8c{m}^2$

Answer 1

The correct option is C $3.4c{m}^2$

Least count $=\frac{0.5}{50}mm=0.01mm$

$\therefore$ Diameter, $d=1.5mm+7\times 0.01$

$=1.57mm$

$\therefore$ Surface area $=\left(2\pi r\right)\times l$

$=\pi dl$

$=3.142\times \frac{1.57}{10}\times 6.8c{m}^2$

$=3.354c{m}^2=3.4c{m}^2$