The density of the material of a wire used in sonometer is `75xx10^(-2) kg //m^(3)`. If the stress on the wire is `3.0xx10^(4) N//m^(2)`, the speed of transverse wave in the wire will be

Options

A. 100 m/s
B. 200 m/s
C. 300 m/s
D. 400 m/s

Explanation

To find the speed of transverse waves in the wire, we can use the formula derived from Newton's laws, which states:

\[ V = \sqrt{\frac{\text{Stress}}{\text{Density}}} \]

Where:
- \( V \) is the speed of the wave,
- Stress is given in \( N/m^2 \),
- Density is given in \( kg/m^3 \).

### Step-by-step Solution:

1. **Identify the given values**:
- Density (\( \rho \)) = \( 75 \times 10^{-2} \, kg/m^3 \)
- Stress (\( \sigma \)) = \( 3.0 \times 10^{4} \, N/m^2 \)

2. **Substitute the values into the formula**:
\[ V = \sqrt{\frac{3.0 \times 10^{4}}{75 \times 10^{-2}}} \]

3. **Simplify the denominator**:
- Convert \( 75 \times 10^{-2} \) to \( 0.75 \):
\[ V = \sqrt{\frac{3.0 \times 10^{4}}{0.75}} \]

4. **Calculate the division**:
\[ \frac{3.0 \times 10^{4}}{0.75} = 4.0 \times 10^{4} \]

5. **Take the square root**:
\[ V = \sqrt{4.0 \times 10^{4}} = \sqrt{4} \times \sqrt{10^{4}} = 2 \times 10^{2} = 200 \, m/s \]

6. **Final Result**:
The speed of the transverse wave in the wire is \( 200 \, m/s \).