# A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading=6mm. Circular scale reading=64 divisions. Given that 1 mm on main scale corresponds to 100 divisions of circular scale.What is the diameter of wire?

Mar 26, 2018

The diameter of the wire $= \text{6.64 mm" = "0.664 cm}$.

#### Explanation:

The screw gauge has the main scale in $\text{mm}$, so one rotation opens up $\text{1 mm}$. But

$\text{one rotation = 100 divisions on the cap = 1mm}$

Therefore, the least count of the screw gauge $=$ the distance moved by rotation of one div on the cap.

$= \left(\frac{1}{100}\right) \setminus \text{mm" = "0.01 mm}$

The reading of the diameter is

$D = \text{main scale (in mm)" + "cap scale reading" xx "least count}$

$D = \text{6 mm" + (64xx 0.01 ) \ "mm}$

$D = \text{6.64 mm}$