Least count of a vernier calliper is 0.01 cm. While measuring the length of any object, the reading of main scale is 2.7 cm and 5th mark of vernier is in line with any mark of main scale. What is the length of that object?

Options

A. 2.75 cm
B. 3.75 cm
C. 1.75 cm
D. 4.75 cm

Explanation

To find the length of the object using a vernier caliper, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Main Scale Reading (MSR)**:
- The reading on the main scale is given as 2.7 cm.

2. **Identify the Vernier Scale Reading (VSR)**:
- The problem states that the 5th mark of the vernier scale is in line with a mark on the main scale. This means the Vernier Scale Reading (VSR) is 5.

3. **Determine the Least Count (LC)**:
- The least count of the vernier caliper is given as 0.01 cm.

4. **Calculate the Total Reading**:
- The formula to calculate the total length (L) using the readings is:
\[ L = \text{MSR} + (\text{VSR} \times \text{LC}) \]
- Substituting the values:
\[ L = 2.7 \, \text{cm} + (5 \times 0.01 \, \text{cm}) \]
- Calculate the Vernier contribution:
\[ 5 \times 0.01 \, \text{cm} = 0.05 \, \text{cm} \]
- Now, add this to the main scale reading:
\[ L = 2.7 \, \text{cm} + 0.05 \, \text{cm} = 2.75 \, \text{cm} \]

5. **Final Result**:
- The length of the object is **2.75 cm**.