Question

If 50 Vernier divisions are equal to 49 main scale divisions of a travelling microscope and one smallest reading of the main scale is 0.5 mm, the Vernier constant of the travelling microscope is:

• A. 0.01 mm
• B. 0.1 mm
• C. 0.1 cm
• D. 0.01 cm

Answer 1

The Correct Option is A

The Vernier constant (VC) is calculated as:

\[ \text{VC} = \text{Value of 1 MSD} - \text{Value of 1 VSD} \]

Given that 50 Vernier divisions correspond to 49 main scale divisions:

- The value of 1 MSD is 0.5 mm.
- Therefore, the value of 1 VSD is:

\[ \text{Value of 1 VSD} = \frac{49 \times 0.5 \text{ mm}}{50} = 0.49 \text{ mm} \]

Calculating the VC:

\[ \text{VC} = 0.5 \text{ mm} - 0.49 \text{ mm} = 0.01 \text{ mm} \]

Answer 2

This problem requires us to calculate the Vernier constant (which is the same as the least count) of a travelling microscope, given the relationship between its main scale divisions and Vernier scale divisions.

Concept Used:

The Vernier constant (VC) or Least Count (LC) of a Vernier instrument is the smallest measurement that can be accurately made with the instrument. It is defined as the difference between the value of one main scale division (MSD) and one Vernier scale division (VSD).

\[ \text{Vernier Constant (VC)} = \text{Value of 1 MSD} - \text{Value of 1 VSD} \]

To use this formula, we first need to find the value of one Vernier scale division (VSD) using the given relationship between the two scales.

Step-by-Step Solution:

Step 1: Identify the given information from the problem statement.

We are given:

• The value of the smallest division on the main scale, which is the value of one main scale division (1 MSD). \[ 1 \text{ MSD} = 0.5 \text{ mm} \]
• The relationship between the main scale and the Vernier scale: 50 divisions on the Vernier scale coincide with 49 divisions on the main scale. \[ 50 \text{ VSD} = 49 \text{ MSD} \]

Step 2: Calculate the value of one Vernier scale division (1 VSD).

Using the given relationship, we can express the value of 1 VSD in terms of MSD.

\[ 50 \text{ VSD} = 49 \text{ MSD} \]

Dividing both sides by 50, we get:

\[ 1 \text{ VSD} = \frac{49}{50} \text{ MSD} \]

Now, we substitute the given value of 1 MSD = 0.5 mm to find the value of 1 VSD in millimeters.

\[ 1 \text{ VSD} = \frac{49}{50} \times 0.5 \text{ mm} = 0.98 \times 0.5 \text{ mm} = 0.49 \text{ mm} \]

Step 3: Calculate the Vernier constant (LC).

Using the formula for the Vernier constant:

\[ \text{LC} = 1 \text{ MSD} - 1 \text{ VSD} \]

Substitute the values we have for 1 MSD and 1 VSD:

\[ \text{LC} = 0.5 \text{ mm} - 0.49 \text{ mm} \]

Final Computation & Result:

Performing the final subtraction gives us the Vernier constant.

\[ \text{LC} = 0.01 \text{ mm} \]

The Vernier constant of the travelling microscope is 0.01 mm.