Question

In an experiment the angles are required to be measured using an instrument. 29 division of the main scale exactly coincide with the 30 division of the vernier scale. If the smallest division of the main scale is half-a-degree ( $=0.5°$), then the least count of the instrument is

• A. one minute
• B. half minute
• C. one degree
• D. half degree

Answer 1

The correct option is A

one minute

Explanation for correct option:
Option (a) one minute

Step 1: Given data

29 divisions of main scale coincide with 30 divisions of Vernier scale

$1\mathrm{MSD}=0.5°$

Step 2: Formula used

To answer this question, we will use the least count formula in terms of VSD and MSD, i.e.,

Least count $=1\mathrm{MSD}-1\mathrm{VSD}$

Step 3: Find the least count of the instrument

By using the given parameters in the above formula
We have

Least count $=1\mathrm{MSD}-\frac{29}{30}\mathrm{MSD}$

Least count $=\frac{1}{30}\mathrm{MSD}$

Least count $=\frac{1}{30}\times 0.5°$

Least count $=\frac{1}{30}\times 30\min$

Least count $=1\min$

Hence, the least count of the instrument is one minute, so, option (a) is correct.