If the load of a wire is increases such that its stress is twice as that of previous, then the new value of Young`s modulus is

Options

A. Increases
B. Remain same
C. Decreases
D. May increases or decreases

Answer

To solve the problem, we need to understand the relationship between stress, strain, and Young's modulus.

### Step-by-Step Solution:

1. **Understanding Young's Modulus**:
Young's modulus (E) is defined as the ratio of stress (σ) to strain (ε):
\[ E = \frac{\sigma}{\epsilon} \]
where stress (σ) is the force (F) applied per unit area (A), and strain (ε) is the change in length (ΔL) divided by the original length (L).

2. **Initial Conditions**:
Let the initial stress be σ₁ and the corresponding strain be ε₁. Therefore, we can write:
\[ E = \frac{\sigma_1}{\epsilon_1} \]

3. **New Conditions**:
According to the problem, the new stress (σ₂) is twice the initial stress:
\[ \sigma_2 = 2\sigma_1 \]

4. **Effect on Strain**:
If the stress is doubled, we need to consider how strain changes. In many materials, especially those that follow Hooke's law (which is applicable for small deformations), strain is directly proportional to stress. Therefore, if stress is doubled, strain will also double:
\[ \epsilon_2 = 2\epsilon_1 \]

5. **Calculating New Young's Modulus**:
Now, we can calculate the new Young's modulus (E₂) using the new stress and strain:
\[ E_2 = \frac{\sigma_2}{\epsilon_2} = \frac{2\sigma_1}{2\epsilon_1} = \frac{\sigma_1}{\epsilon_1} = E \]

6. **Conclusion**:
The new value of Young's modulus remains the same as the original value:
\[ E_2 = E \]

### Final Answer:
The new value of Young's modulus is the same as the previous value.