Question

The pitch of a screw gauge is 1 mm and the circular scale has 100 divisions. In measuring the diameter of a wire, the main scale reads 3 mm and 43 mark on the circular scale. Find the:

1. Least count
2. The radius of the wire

Answer 1

Step 1: Given data

Pitch of the screw gauge$=1mm$

Number of divisions on a circular scale$=100$

Main scale reading$=3mm$

Number of divisions of the circular head with baseline$=43$

Step 2: Calculating least count

$$\begin{gathered} Leastcount=\frac{Pitch}{No.ofdivisionsonacircularscale} \\ =\frac{1mm}{100} \\ =0.01mm=0.001cm \end{gathered}$$

Hence least count is 0.001 cm

Step 3: Circular scale reading

$$\begin{gathered} Circularscalereading=p\times leastcount \\ =43\times 0.001 \\ =0.043cm \end{gathered}$$

Hence circular scale reading is 0.043 cm

Step 4:Total scale reading

$$\begin{gathered} Totalscalerading=Mainscalereading+Circularscalereading \\ =0.3cm+0.043cm \\ =0.343cm \end{gathered}$$

Hence, the total scale reading is 0.343 cm.

Step 5: Diameter of wire

$$\begin{gathered} Totalscalereading=Diameterofawire \\ 0.343cm=Diameterofawire \end{gathered}$$

Hence, the diameter of a wire is 0.343 cm.

Step 6:Radius of wire

$$\begin{gathered} Radiusofwire=\frac{Diameterofwire}{2} \\ =\frac{0.343cm}{2} \\ =0.1715cm \end{gathered}$$

Hence, the radius of a wire is 0.1715 cm.

Hence, the least count is 0.001 cm and the radius of the wire is 0.1715 cm.