The least count of a vernier callipers is :

Options

A. 1 cm
B. 0.001 cm
C. 0.1 cm
D. 0.01 cm

Explanation

To determine the least count of a vernier caliper, we can follow these steps:

### Step 1: Understand the Components
The least count of a vernier caliper is defined as the smallest measurement that can be accurately read using the instrument. It is calculated based on the difference between one main scale division (MSD) and one vernier scale division (VSD).

### Step 2: Identify the Values
Typically, in a vernier caliper:
- The main scale division (MSD) is usually 1 cm (which is equivalent to 10 mm).
- The vernier scale is designed to provide a finer measurement than the main scale.

### Step 3: Calculate the Least Count
The formula for the least count (LC) of a vernier caliper is:
\[ \text{Least Count (LC)} = \text{1 MSD} - \text{1 VSD} \]

Assuming:
- 1 MSD = 1 cm = 10 mm
- 1 VSD = 0.9 mm (which is common for a vernier caliper with 10 divisions on the vernier scale)

Thus, we can calculate:
\[ \text{LC} = 1 \text{ MSD} - \text{1 VSD} = 1 \text{ cm} - 0.9 \text{ mm} \]
Converting 1 cm to mm gives us:
\[ 1 \text{ cm} = 10 \text{ mm} \]
So,
\[ \text{LC} = 10 \text{ mm} - 0.9 \text{ mm} = 0.1 \text{ mm} \]
Converting this back to centimeters:
\[ 0.1 \text{ mm} = 0.01 \text{ cm} \]

### Step 4: Conclusion
Therefore, the least count of a vernier caliper is:
\[ \text{Least Count} = 0.01 \text{ cm} \]

The correct option is **D) 0.01 cm**.

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