Two wires have identical lengths and areas of cross-section are suspended by mass `M`. Their Young's modulus are in the ratio `2:5`.

Options

A. They will be subjected to stresses which are in ratio `2:5`
B. Their lengths will increase in the ratio `5:2`
C. When stretched and released, they will oscillate with time periods in the ratio `5:2`
D. Their time periods will be in the ratio `sqrt(5):sqrt(2)`

Explanation

To solve the problem, we need to analyze the relationship between the Young's modulus of the two wires and their time periods when suspended by the same mass \( M \).

### Step-by-Step Solution:

1. **Understanding Young's Modulus**:
Young's modulus \( Y \) is defined as the ratio of stress to strain:
\[
Y = \frac{\text{Stress}}{\text{Strain}} = \frac{\frac{F}{A}}{\frac{\Delta L}{L}} = \frac{F \cdot L}{A \cdot \Delta L}
...