The velocity of transverse wave in string whose linear mass density is `3×10^-2 kg/m` stretched by a load of 30 kg is (Take g=10`m/s^2`)

Options

A. 10m/s
B. 30m/s
C. 300m/s
D. 100m/s

Answer

To find the velocity of a transverse wave in a string with a given linear mass density and stretched by a load, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Linear mass density (μ) = \(3 \times 10^{-2} \, \text{kg/m}\)
- Mass (m) = \(30 \, \text{kg}\)
- Acceleration due to gravity (g) = \(10 \, \text{m/s}^2\)

2. **Calculate the Tension (T):**
- The tension in the string is equal to the weight of the load applied.
- Weight (W) = mass (m) × gravity (g)
- Therefore, \(T = m \cdot g = 30 \, \text{kg} \times 10 \, \text{m/s}^2 = 300 \, \text{N}\)

3. **Use the Formula for Velocity of Transverse Wave:**
- The formula for the velocity (V) of a transverse wave in a string is given by:
\[ V = \sqrt{\frac{T}{\mu}} \]

4. **Substitute the Values into the Formula:**
- Substitute \(T = 300 \, \text{N}\) and \(\mu = 3 \times 10^{-2} \, \text{kg/m}\):
\[ V = \sqrt{\frac{300}{3 \times 10^{-2}}} \]

5. **Simplify the Expression:**
- First, calculate the denominator:
\[ 3 \times 10^{-2} = 0.03 \]
- Now, divide:
\[ \frac{300}{0.03} = 10000 \]

6. **Calculate the Square Root:**
- Now take the square root:
\[ V = \sqrt{10000} = 100 \, \text{m/s} \]

### Final Answer:
The velocity of the transverse wave in the string is \(100 \, \text{m/s}\).

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