If the length of a body is measured in centimeters instead of meters, the coefficient of linear expansion

Options

A. increases
B. decreases
C. remains same
D. decreases to 1/100 of the original value

Answer

To solve the question regarding the effect of measuring the length of a body in centimeters instead of meters on the coefficient of linear expansion, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Coefficient of Linear Expansion**:
The coefficient of linear expansion (α) is defined as the fractional change in length per degree change in temperature. It is a material property and does not depend on the units used for measuring length.

2. **Measurement Units**:
When measuring length, we can use different units such as meters or centimeters. For example, if a rod has a length of 75 cm, it can also be expressed as 0.75 m. The numerical value of the length changes with the unit, but the physical property (length) remains the same.

3. **Effect on Coefficient of Linear Expansion**:
Since the coefficient of linear expansion is a ratio (change in length/original length), changing the unit of measurement does not affect the value of α. Whether we express the length in centimeters or meters, the ratio remains unchanged.

4. **Conclusion**:
Therefore, the coefficient of linear expansion remains the same regardless of whether the length is measured in centimeters or meters.

5. **Final Answer**:
The correct option is that the coefficient of linear expansion remains the same.