The main scale of vernier callipers is divided into `0.5mm` and its least count is `0.005 cm`. Then the number of divisions on vernier scale is

Options

A. `10`
B. `20`
C. `30`
D. `40`

Explanation

To find the number of divisions on the vernier scale, we can follow these steps:

### Step 1: Convert the least count to the same unit as the main scale
The least count is given as `0.005 cm`. We need to convert this to millimeters (mm) since the main scale is in mm.

\[ 0.005 \text{ cm} = 0.005 \times 10 \text{ mm} = 0.05 \text{ mm} \]

### Step 2: Identify the value of one main scale division (MSD)
The main scale of the vernier callipers is divided into `0.5 mm`. Therefore,

\[ \text{MSD} = 0.5 \text{ mm} \]

### Step 3: Use the formula for least count
The least count (LC) of a vernier caliper is given by the formula:

\[ \text{LC} = \frac{\text{MSD}}{n} \]

where \( n \) is the number of divisions on the vernier scale.

### Step 4: Rearrange the formula to find \( n \)
We can rearrange the formula to solve for \( n \):

\[ n = \frac{\text{MSD}}{\text{LC}} \]

### Step 5: Substitute the values
Now, we substitute the values we have:

\[ n = \frac{0.5 \text{ mm}}{0.05 \text{ mm}} = 10 \]

### Conclusion
The number of divisions on the vernier scale is \( n = 10 \).

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