Question

The length is measured using a vernier system whose main scale is 30 cm long with 600 divisions. If 19 divisions of the main scale coincide with 20 divisions of the vernier scale, then its least count is

• A. 0.25 cm
• B. 0.025 cm
• C. 0.25 mm
• D. 0.025 mm
• E. 0.0025 mm

Hint:

Least Count is simply $\frac{\text{Value of 1 MSD}}{\text{Total number of divisions on Vernier Scale}}$ if $n = m-1$.

Answer 1

The Correct Option is D

Concept:
The Least Count (LC) of a Vernier Caliper is the difference between one Main Scale Division (MSD) and one Vernier Scale Division (VSD). \[ LC = 1 MSD - 1 VSD = 1 MSD \times \left(1 - \frac{n}{m}\right) \] where $n$ main scale divisions coincide with $m$ vernier scale divisions.

Step 1: Find the value of one Main Scale Division (MSD).
The main scale is 30 cm long and has 600 divisions. \[ 1 MSD = \frac{30 \text{ cm}}{600} = \frac{3 \text{ mm} \times 100}{600} = 0.05 \text{ cm} = 0.5 \text{ mm} \]

Step 2: Apply the Least Count formula.
Given: 19 MSD = 20 VSD $\Rightarrow 1 VSD = \frac{19}{20} MSD$. \[ LC = 1 MSD - 1 VSD = 1 MSD - \frac{19}{20} MSD = \frac{1}{20} MSD \] \[ LC = \frac{1}{20} \times 0.5 \text{ mm} = 0.025 \text{ mm} \]