What is the edge length of the cube?
There is one vernier caliper in which 1 main scale division (MSD) is 1mm. It is given that 10 divisions of vernier scale match with 9 divisions of main scale. Given vernier caliper is used to measure the edge of a cube. Main scale reading (MSR) was found to be 10 and first division of the vernier scale was found to be coinciding with some division of the main scale. Mass of the cube is 2.736g.

Options

A. `1.01mm`
B. `1.01cm`
C. `10.1cm`
D. `1.001cm`

Explanation

To find the edge length of the cube using the given information about the vernier caliper, we will follow these steps:

### Step 1: Understand the Vernier Caliper Specifications
- The main scale division (MSD) is 1 mm.
- 10 divisions of the vernier scale (VSD) match with 9 divisions of the main scale.

### Step 2: Calculate the Least Count (LC)
The least count of the vernier caliper can be calculated using the formula:
\[ \text{Least Count (LC)} = \text{MSD} - \text{VSD} \]
From the information given:
- 10 VSD = 9 MSD
- Therefore, 1 VSD = \( \frac{9}{10} \) MSD = 0.9 mm.

Now, substituting the values:
\[ \text{LC} = 1 \text{ mm} - 0.9 \text{ mm} = 0.1 \text{ mm} \]

### Step 3: Read the Measurements
- The main scale reading (MSR) is given as 10 mm.
- The first division of the vernier scale coincides with the main scale, which corresponds to 1 VSD.

### Step 4: Calculate the Final Reading
The final reading can be calculated using the formula:
\[ \text{Final Reading} = \text{MSR} + (\text{Vernier Scale Reading} \times \text{Least Count}) \]
Substituting the values:
- MSR = 10 mm
- Vernier Scale Reading = 1 (since the first division is coinciding)
- LC = 0.1 mm

Now, substituting these into the formula:
\[ \text{Final Reading} = 10 \text{ mm} + (1 \times 0.1 \text{ mm}) = 10 \text{ mm} + 0.1 \text{ mm} = 10.1 \text{ mm} \]

### Step 5: Convert to Centimeters
To convert the edge length from mm to cm:
\[ 10.1 \text{ mm} = \frac{10.1}{10} \text{ cm} = 1.01 \text{ cm} \]

### Conclusion
The edge length of the cube is **1.01 cm**.

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