A string of mass 3 kg is under tension of 400 N. the length of the stretched string is 25 cm. if the transverse jerk is stuck at one end of the string how long does the disturbance take to reach the other end?

Options

A. 0.043s
B. 4.33S
C. 0.055 s
D. 0.034 s

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Identify the given values
- Mass of the string (m) = 3 kg
- Tension in the string (T) = 400 N
- Length of the string (L) = 25 cm = 0.25 m

### Step 2: Calculate the mass per unit length (μ)
The mass per unit length (μ) is given by the formula:
\[ \mu = \frac{m}{L} \]
Substituting the values:
\[ \mu = \frac{3 \, \text{kg}}{0.25 \, \text{m}} = 12 \, \text{kg/m} \]

### Step 3: Calculate the speed of the wave (v) on the string
The speed of the wave on the string is given by the formula:
\[ v = \sqrt{\frac{T}{\mu}} \]
Substituting the values:
\[ v = \sqrt{\frac{400 \, \text{N}}{12 \, \text{kg/m}}} \]
Calculating this gives:
\[ v = \sqrt{33.33} \approx 5.77 \, \text{m/s} \]

### Step 4: Calculate the time taken for the disturbance to reach the other end
The time (t) taken for the disturbance to travel the length of the string is given by:
\[ t = \frac{L}{v} \]
Substituting the values:
\[ t = \frac{0.25 \, \text{m}}{5.77 \, \text{m/s}} \approx 0.043 \, \text{s} \]

### Conclusion
The time taken for the disturbance to reach the other end of the string is approximately **0.043 seconds**.

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