`1 cm` on the main scale of a vernier calipers is divided into `10 equal` parts. If `10` divisions of vernier coincide with `8` small divisions of main scale, then the least count of the caliper is.

Options

A. (a)0 .01 cm
B. (b)0.02 cm
C. (c)0.05 cm
D. (d)0.005 cm

Explanation

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

### Step 1: Determine the value of one main scale division (MSD).
1. We know that 1 cm on the main scale is divided into 10 equal parts.
2. Therefore, the value of one main scale division (MSD) is:
\[ \text{MSD} = \frac{1 \text{ cm}}{10} = 0.1 \text{ cm} \]

### Step 2: Determine the value of one vernier scale division (VSD).
1. According to the problem, 10 divisions of the vernier scale coincide with 8 divisions of the main scale.
2. This means:
\[ 10 \text{ VSD} = 8 \text{ MSD} \]
3. To find the value of one vernier scale division (VSD), we can rearrange this equation:
\[ \text{VSD} = \frac{8 \text{ MSD}}{10} = \frac{8 \times 0.1 \text{ cm}}{10} = 0.08 \text{ cm} \]

### Step 3: Calculate the least count (LC) of the vernier calipers.
1. The least count of the vernier calipers is given by the formula:
\[ \text{Least Count (LC)} = \text{MSD} - \text{VSD} \]
2. Substituting the values we found:
\[ \text{LC} = 0.1 \text{ cm} - 0.08 \text{ cm} = 0.02 \text{ cm} \]

### Conclusion:
The least count of the vernier calipers is \(0.02 \text{ cm}\).

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