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: Identify the smallest division on the main scale
The smallest division on the main scale (MSD) of the Vernier calipers is given as 0.5 mm.

### Step 2: Identify the number of divisions on the Vernier scale
The Vernier scale has 25 divisions (VSD = 25).

### Step 3: Identify the number of divisions on the main scale that coincide with the Vernier scale
The Vernier scale divisions coincide with 24 divisions of the main scale (MSD = 24).

### Step 4: Calculate the value of one division of the Vernier scale
Since 25 divisions of the Vernier scale coincide with 24 divisions of the main scale, we can express this mathematically:
\[ \text{Length of 25 VSD} = \text{Length of 24 MSD} \]
\[ 25 \times \text{VSD} = 24 \times 0.5 \text{ mm} \]
\[ \text{VSD} = \frac{24 \times 0.5 \text{ mm}}{25} = \frac{12 \text{ mm}}{25} = 0.48 \text{ mm} \]

### Step 5: Calculate the least count of the Vernier calipers
The least count (LC) of the Vernier calipers is given by the formula:
\[ \text{Least Count} = \text{MSD} - \text{VSD} \]
Substituting the values we have:
\[ \text{Least Count} = 0.5 \text{ mm} - 0.48 \text{ mm} = 0.02 \text{ mm} \]

### Step 6: Convert the least count to centimeters
To 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 **0.002 cm**.

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