If in a Vernier callipers 10 VSD coincides with 8 MSD, then the least count of Vernier calliper is [given 1 MSD = 1mm]

Options

A. `1xx10^(-4)m`
B. `2xx10^(-4)m`
C. `1xx10^(-3)m`
D. `8xx10^(-4)m`

Answer

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

### Step 1: Understand the relationship between Vernier scale divisions (VSD) and main scale divisions (MSD).
We are given that 10 VSD coincide with 8 MSD. This means:
\[ 10 \text{ VSD} = 8 \text{ MSD} \]

### Step 2: Calculate the value of one VSD in terms of MSD.
To find the value of one VSD, we can divide both sides of the equation by 10:
\[ 1 \text{ VSD} = \frac{8 \text{ MSD}}{10} = 0.8 \text{ MSD} \]

### Step 3: Convert VSD to millimeters.
Since we know that 1 MSD = 1 mm, we can substitute this into our equation:
\[ 1 \text{ VSD} = 0.8 \text{ MSD} = 0.8 \text{ mm} \]

### Step 4: Use the formula for least count of the Vernier caliper.
The formula for the least count (LC) of a Vernier caliper is given by:
\[ \text{Least Count} = \text{Value of 1 MSD} - \text{Value of 1 VSD} \]
Substituting the known values:
\[ \text{Least Count} = 1 \text{ MSD} - 1 \text{ VSD} = 1 \text{ mm} - 0.8 \text{ mm} \]

### Step 5: Calculate the least count.
Now, performing the subtraction:
\[ \text{Least Count} = 1 \text{ mm} - 0.8 \text{ mm} = 0.2 \text{ mm} \]

### Step 6: Convert the least count to scientific notation.
To express 0.2 mm in scientific notation:
\[ 0.2 \text{ mm} = 2 \times 10^{-1} \text{ mm} \]
Since 1 mm = \(1 \times 10^{-3}\) meters, we can convert it:
\[ 0.2 \text{ mm} = 0.2 \times 10^{-3} \text{ m} = 2 \times 10^{-4} \text{ m} \]

### Final Answer:
The least count of the Vernier caliper is:
\[ \text{Least Count} = 2 \times 10^{-4} \text{ m} \]

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