If 25venier scale divisions coincide with 20 main scale divisions. Find least count of venier calliper. ( One main scale division = 1mm )

Options

A. 0.02cm
B. 0.02 cm
C. 0.01 cm
D. 0.01 mm

Explanation

To find the least count of the vernier caliper, we will follow these steps:

### Step 1: Understand the given information
We know that:
- 1 main scale division (MSD) = 1 mm
- 25 vernier scale divisions (VSD) coincide with 20 main scale divisions (MSD).

### Step 2: Find the value of one vernier scale division (VSD)
From the information given:
\[ 25 \, \text{VSD} = 20 \, \text{MSD} \]

To find 1 VSD, we can divide both sides by 25:
\[ 1 \, \text{VSD} = \frac{20 \, \text{MSD}}{25} \]
\[ 1 \, \text{VSD} = \frac{20}{25} \, \text{MSD} \]
\[ 1 \, \text{VSD} = \frac{4}{5} \, \text{MSD} \]

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

Substituting the values we have:
\[ \text{LC} = 1 \, \text{MSD} - \frac{4}{5} \, \text{MSD} \]
\[ \text{LC} = 1 - \frac{4}{5} \, \text{MSD} \]
\[ \text{LC} = \frac{1}{5} \, \text{MSD} \]

### Step 4: Substitute the value of MSD
Since 1 MSD = 1 mm, we substitute:
\[ \text{LC} = \frac{1}{5} \, \text{mm} \]
\[ \text{LC} = 0.2 \, \text{mm} \]

### Step 5: Convert to centimeters (if needed)
To convert millimeters to centimeters:
\[ 0.2 \, \text{mm} = 0.02 \, \text{cm} \]

### Final Answer
The least count of the vernier caliper is:
\[ \text{LC} = 0.2 \, \text{mm} \text{ or } 0.02 \, \text{cm} \]

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