Question

While measuring the length of a copper rod using a vernier caliper. the zero of the vernier scale was found to be between $4.6\mathrm{cm}$and $4.7\mathrm{cm}$on the main scale. The $6\mathrm{th}$division of the vernier scale is found to coincide with a division on the main scale. Find the length of the rod if the least count is $0.01\mathrm{cm}$

Answer 1

Step 1:- Given data

The least count of the vernier caliper$=0.01\mathrm{cm}$

$=0.1\mathrm{mm}$

Main Scale Reading is between $=4.6\mathrm{cm}\mathrm{and}4.7\mathrm{cm}$

$=46\mathrm{mm}\mathrm{and}47\mathrm{mm}$

Vernier coinciding division $=6$(with the division on the main scale).

Step 2:- Formula for vernier caliper:

Length of the rod = Main scale reading + (Vernier caliper reading x Least count)

$$\begin{gathered} \mathrm{Length}=\mathrm{MSR}+(\mathrm{VSR}\times \mathrm{L}.\mathrm{C}) \\ =46+6\times 0.1 \end{gathered}$$

$=46.6\mathrm{mm}$

Hence, the length of the rod will be$46.6\mathrm{mm}\mathrm{or}4.66\mathrm{cm}$