In a given slide callipers 10 division of its vernier coincides with its 9 main scale divisions. If one main scale division is equal to 0.5 mm then find its least count.

Explanation

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

### Step 1: Understand the relationship between the Vernier scale and the main scale.
We know that 10 divisions of the Vernier scale coincide with 9 divisions of the main scale. This means that the length represented by 10 Vernier divisions is equal to the length represented by 9 main scale divisions.

### Step 2: Calculate the value of one Vernier scale division.
Let’s denote:
- \( \text{MSD} \) = Main Scale Division
- \( \text{VSD} \) = Vernier Scale Division

From the problem, we have:
\[ 10 \, \text{VSD} = 9 \, \text{MSD} \]
To find the value of one Vernier scale division, we can express it as:
\[ \text{VSD} = \frac{9}{10} \, \text{MSD} \]

### Step 3: Substitute the value of the Main Scale Division.
We know that:
\[ 1 \, \text{MSD} = 0.5 \, \text{mm} \]
Now substituting this value into the equation for VSD:
\[ \text{VSD} = \frac{9}{10} \times 0.5 \, \text{mm} = 0.45 \, \text{mm} \]

### Step 4: Calculate the Least Count (LC).
The least count is given by the formula:
\[ \text{LC} = \text{MSD} - \text{VSD} \]
Substituting the values we have:
\[ \text{LC} = 0.5 \, \text{mm} - 0.45 \, \text{mm} = 0.05 \, \text{mm} \]

### Final Answer:
The least count of the slide calipers is \( 0.05 \, \text{mm} \).

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