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 solve the problem, we will follow these steps:

### Step 1: Determine the Least Count of the Vernier Caliper
The least count (LC) of the vernier caliper can be calculated using the formula:

\[ \text{Least Count (LC)} = \text{Value of 1 MSD} - \text{Value of 1 VSD} \]

Given that the vernier scale has 8 divisions that coincide with 7 divisions of the main scale, we can express this as:

\[ 1 \text{ VSD} = \frac{7}{8} \text{ MSD} \]

Since 1 MSD (Main Scale Division) is 1 mm, we have:

\[ 1 \text{ VSD} = \frac{7}{8} \text{ mm} \]

Now, substituting this into the least count formula:

\[ \text{LC} = 1 \text{ mm} - \frac{7}{8} \text{ mm} = \frac{1}{8} \text{ mm} = 0.125 \text{ mm} \]

### Step 2: Read the Main Scale Reading (MSR)
The main scale reading is given directly in the problem:

\[ \text{MSR} = 12 \text{ mm} \]

### Step 3: Read the Vernier Scale Reading (VSR)
The problem states that the second division of the vernier scale coincides with the main scale. Therefore, we calculate the vernier scale reading as:

\[ \text{VSR} = n \times \text{LC} \]

Where \( n \) is the division number of the vernier scale that coincides with the main scale. Here, \( n = 2 \):

\[ \text{VSR} = 2 \times 0.125 \text{ mm} = 0.250 \text{ mm} \]

### Step 4: Calculate Zero Correction
Since the problem states that the zero of the vernier scale coincides with the zero of the main scale when the jaws are in contact, the zero correction is:

\[ \text{Zero Correction} = 0 \text{ mm} \]

### Step 5: Calculate the Final Reading
Now, we can find the total reading using the formula:

\[ \text{Total Reading} = \text{MSR} + \text{VSR} + \text{Zero Correction} \]

Substituting the values we found:

\[ \text{Total Reading} = 12 \text{ mm} + 0.250 \text{ mm} + 0 \text{ mm} = 12.250 \text{ mm} \]

### Final Answer
The edge length of the cube is:

\[ \text{Edge Length} = 12.250 \text{ mm} \]

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