Rigidity modulus of steel is `eta` and its Young's modulus is Y. A piece of steel of cross sectional area A is chaged into a wire of length L and area `(A)/(10)` then :

Options

A. Y increases and `eta` decreases
B. Y and `eta` remain the same
C. both Y and `eta` increase
D. boty Y and `eta` decrease

Explanation

To solve the problem, we need to analyze the properties of the steel piece when it is transformed into a wire. We are given that the rigidity modulus of steel is \( \eta \) and its Young's modulus is \( Y \). The original piece of steel has a cross-sectional area \( A \) and is changed into a wire of length \( L \) and a new cross-sectional area \( \frac{A}{10} \).

### Step-by-Step Solution:

1. **Understanding Young's Modulus**:
Young's modulus \( Y \) is defined as the ratio of tensile stress to tensile strain. It is a property that depends on the material itself and not on its dimensions.

\[ Y = \frac{\text{Tensile Stress}}{\text{Tensile Strain}} = \frac{F/A}{\Delta L/L} \]

where \( F \) is the force applied, \( A \) is the cross-sectional area, \( \Delta L \) is the change in length, and \( L \) is the original length.

2. **Understanding Rigidity Modulus**:
The rigidity modulus \( \eta \) (or shear modulus) is defined as the ratio of shear stress to shear strain. Like Young's modulus, it is also a material property.

3. **Change in Dimensions**:
When the steel piece is transformed into a wire, its dimensions change. The length of the wire becomes \( L \) and the new cross-sectional area becomes \( \frac{A}{10} \).

4. **Effect on Young's Modulus**:
Since Young's modulus is a property of the material, it remains constant regardless of the changes in dimensions. Therefore, after changing the dimensions, the Young's modulus of the wire will still be \( Y \).

5. **Effect on Rigidity Modulus**:
Similarly, the rigidity modulus \( \eta \) is also a property of the material. Thus, it will also remain unchanged after the transformation.

6. **Conclusion**:
The Young's modulus and rigidity modulus of the steel wire remain the same as that of the original piece of steel. Therefore, the answer to the question is that both Young's modulus and rigidity modulus remain \( Y \) and \( \eta \) respectively.

### Final Answer:
- Young's Modulus remains \( Y \).
- Rigidity Modulus remains \( \eta \).