The main scale of a vernier calliper reads in mm and its vernier scale is divided into 8 divisions, which coincides with 7 divisions of the main scale. It was also observed that, when the two jaws are brought in contact, the zero of the vernier scale coincided with the zero of the main scale. The edge length of a cube is measured using this vernier calliper. The main scale reads 12 mm and `2^("nd")` division of the vernier scale coincides with the main scale. The edge length (in mm) of the cube is

Answer

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

### Step 1: Understand the given information
- The main scale of the vernier caliper reads in mm.
- The vernier scale has 8 divisions that coincide with 7 divisions of the main scale.
- The zero of the vernier scale coincides with the zero of the main scale when the jaws are in contact.
- The main scale reading (MSR) is 12 mm.
- The 2nd division of the vernier scale (VSR) coincides with the main scale.

### Step 2: Calculate the value of one vernier scale division (VSD)
Since 8 divisions of the vernier scale coincide with 7 divisions of the main scale, we can express this as:
\[ 1 \text{ VSD} = \frac{7 \text{ MSR}}{8} = \frac{7 \text{ mm}}{8} = 0.875 \text{ mm} \]

### Step 3: Calculate the least count (LC) of the vernier caliper
The least count is given by the formula:
\[ \text{Least Count (LC)} = \text{1 MSR} - \text{1 VSD} \]
Substituting the values:
\[ \text{LC} = 1 \text{ mm} - \frac{7 \text{ mm}}{8} = 1 \text{ mm} - 0.875 \text{ mm} = 0.125 \text{ mm} \]

### Step 4: Calculate the total length of the cube
The total length (L) of the cube can be calculated using the formula:
\[ L = \text{MSR} + (\text{VSR} \times \text{LC}) \]
Here, the main scale reading (MSR) is 12 mm, and the vernier scale reading (VSR) is the 2nd division, which is 2. Therefore:
\[ L = 12 \text{ mm} + (2 \times 0.125 \text{ mm}) = 12 \text{ mm} + 0.25 \text{ mm} = 12.25 \text{ mm} \]

### Final Answer
The edge length of the cube is **12.25 mm**.

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