A string of mass 2.50kg is under a tension os 200N. The length of the stretched string is 20.0m. If the transverse jerk is struck at one end of the string, how long does the disturbance take to reach the other end?

Options

A. one second
B. 0.5 second
C. 2 second
D. data given is insufficent

Explanation

To solve the problem, we will follow these steps:

### Step 1: Identify the given data
- Mass of the string, \( m = 2.50 \, \text{kg} \)
- Tension in the string, \( T = 200 \, \text{N} \)
- Length of the string, \( L = 20.0 \, \text{m} \)

### Step 2: Calculate the mass per unit length (\( \mu \))
The mass per unit length (\( \mu \)) is calculated using the formula:
\[ \mu = \frac{m}{L} \]
Substituting the values:
\[ \mu = \frac{2.50 \, \text{kg}}{20.0 \, \text{m}} = 0.125 \, \text{kg/m} \]

### Step 3: Calculate the velocity of the wave (\( V \))
The velocity of the transverse wave in the string is given by the formula:
\[ V = \sqrt{\frac{T}{\mu}} \]
Substituting the values:
\[ V = \sqrt{\frac{200 \, \text{N}}{0.125 \, \text{kg/m}}} \]
Calculating the value:
\[ V = \sqrt{1600} = 40 \, \text{m/s} \]

### Step 4: Calculate the time taken for the disturbance to reach the other end
The time taken (\( T \)) for the disturbance to travel the length of the string is given by:
\[ T = \frac{L}{V} \]
Substituting the values:
\[ T = \frac{20.0 \, \text{m}}{40 \, \text{m/s}} = 0.5 \, \text{s} \]

### Final Answer
The disturbance takes **0.5 seconds** to reach the other end of the string.

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