While measuring length of an object it was observed that the zero of the vernier lies between 1.4 and 1.5 of the main scale and the fifth division coincides with a main scale division. If the length of the object measured is l, then the value of (l-1.4) in terms of the least count C of the instrument is:

Options

A. C
B. 1.45C
C. 4C
D. 5C

Explanation

To solve the problem, we need to determine the length of the object measured, denoted as \( l \), and express \( (l - 1.4) \) in terms of the least count \( C \) of the instrument.

### Step-by-step Solution:

1. **Identify the Main Scale Reading (MSR)**:
- The zero of the vernier scale lies between 1.4 and 1.5 on the main scale. Therefore, the main scale reading (MSR) can be taken as:
\[ \text{MSR} = 1.4 \, \text{units} \]

2. **Identify the Vernier Scale Reading (VSR)**:
- It is given that the fifth division of the vernier scale coincides with a main scale division. This means the reading on the vernier scale contributes to the total length measured. The value of the vernier scale reading (VSR) is:
\[ \text{VSR} = 5C \, \text{units} \]
where \( C \) is the least count of the instrument.

3. **Calculate the Total Length (l)**:
- The total length \( l \) can be calculated using the formula:
\[ l = \text{MSR} + \text{VSR} \]
Substituting the values we have:
\[ l = 1.4 + 5C \]

4. **Calculate \( (l - 1.4) \)**:
- Now, we need to find \( (l - 1.4) \):
\[ l - 1.4 = (1.4 + 5C) - 1.4 \]
Simplifying this gives:
\[ l - 1.4 = 5C \]

### Final Result:
Thus, the value of \( (l - 1.4) \) in terms of the least count \( C \) of the instrument is:
\[ l - 1.4 = 5C \]