Smallest division on the main scale of given Vernier calipers is 0.5 mm. Vernier scale has 25 divisions and these coincide with 24 main scale divisions. The least count of Vernier callipers is

Options

A. 0.001 cm
B. 0.002 cm
C. 0.01 cm
D. 0.02 cm

Answer

To find the least count of the Vernier calipers, we can follow these steps:

### Step 1: Understand the given data
- The smallest division on the main scale (MSD) is 0.5 mm.
- The Vernier scale (VD) has 25 divisions that coincide with 24 main scale divisions.

### Step 2: Calculate the value of one Vernier scale division
Since 25 Vernier scale divisions coincide with 24 main scale divisions, we can express the value of one Vernier scale division (VSD) in terms of main scale divisions (MSD):

\[ \text{VSD} = \frac{24 \text{ MSD}}{25} = \frac{24 \times 0.5 \text{ mm}}{25} \]

Calculating this gives:

\[ \text{VSD} = \frac{12 \text{ mm}}{25} = 0.48 \text{ mm} \]

### Step 3: Calculate the least count (LC) of the Vernier calipers
The least count is defined as the difference between one main scale division (MSD) and one Vernier scale division (VSD):

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

Substituting the values we have:

\[ \text{LC} = 0.5 \text{ mm} - 0.48 \text{ mm} = 0.02 \text{ mm} \]

### Step 4: Convert the least count to centimeters
Since the question may require the answer in centimeters, we convert 0.02 mm to centimeters:

\[ 0.02 \text{ mm} = \frac{0.02}{10} \text{ cm} = 0.002 \text{ cm} \]

### Final Answer
Thus, the least count of the Vernier calipers is:

\[ \text{Least Count} = 0.002 \text{ cm} \]

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