10 vernier scale divisions VSD match with 9 main scale divisions MSD. Least count of the given vernier caliper is

Options

A. `0.1 mm " if "1 MSD = 1mm`
B. `0.05 cm " if "1 MSD = 0.05cm`
C. `0.01 mm " if "1 MSD = 1mm`
D. `0.005 cm " if "1 MSD = 0.05cm`

Explanation

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

### Step 1: Understand the relationship between VSD and MSD
We know from the problem statement that 10 Vernier Scale Divisions (VSD) match with 9 Main Scale Divisions (MSD). This can be written as:
\[ 10 \, \text{VSD} = 9 \, \text{MSD} \]

### Step 2: Calculate the value of one VSD in terms of MSD
To find the value of one VSD, we can rearrange the equation:
\[ 1 \, \text{VSD} = \frac{9}{10} \, \text{MSD} \]
This means that one Vernier Scale Division is equal to 0.9 times one Main Scale Division.

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

### Step 4: Substitute the value of VSD into the least count formula
Substituting the value of one VSD from Step 2 into the least count formula:
\[ \text{Least Count} = 1 \, \text{MSD} - 0.9 \, \text{MSD} \]
\[ \text{Least Count} = 0.1 \, \text{MSD} \]

### Step 5: Determine the least count in mm
If we assume that 1 MSD is equal to 1 mm (which is a common assumption), then:
\[ \text{Least Count} = 0.1 \, \text{mm} \]

### Step 6: Verify against the options
Now, let's check the options given:
1. 0.1 mm (Correct)
2. 0.05 cm (Incorrect, as 0.05 cm = 0.5 mm)
3. 0.01 mm (Incorrect)
4. 0.005 cm (Incorrect, as 0.005 cm = 0.05 mm)

Thus, the only correct option is 0.1 mm.

### Final Answer
The least count of the given vernier caliper is **0.1 mm**.

---