A wire is 4 m long and has a mass 0.2 kg. The wire is kept horizontally. A transverse pulse is generated by plucking one end of the taut (tight) wire. The pulse makes four trips back and forth along the cord in 0.8 sec. The tension is the cord will be -

Options

A. 80 N
B. 160 N
C. 240 N
D. 320 N

Answer

To find the tension in the wire, we can follow these steps:

### Step 1: Calculate the total distance traveled by the pulse.
The wire is 4 meters long, and the pulse makes four trips back and forth. Each complete trip consists of going to the end of the wire and returning, which is 8 meters for one trip.

**Total distance covered by the pulse**:
\[ \text{Total distance} = \text{Number of trips} \times \text{Distance for one trip} = 4 \times 8 \text{ m} = 32 \text{ m} \]

### Step 2: Calculate the speed of the pulse.
The time taken for the four trips is given as 0.8 seconds. The speed (v) of the pulse can be calculated using the formula:
\[ v = \frac{\text{Total distance}}{\text{Time}} = \frac{32 \text{ m}}{0.8 \text{ s}} = 40 \text{ m/s} \]

### Step 3: Determine the linear density (μ) of the wire.
The linear density (μ) is defined as the mass per unit length of the wire. Given that the mass of the wire is 0.2 kg and its length is 4 m, we can calculate μ as follows:
\[ \mu = \frac{\text{Mass}}{\text{Length}} = \frac{0.2 \text{ kg}}{4 \text{ m}} = 0.05 \text{ kg/m} \]

### Step 4: Use the wave speed formula to find the tension (T).
The speed of a wave on a string is given by the formula:
\[ v = \sqrt{\frac{T}{\mu}} \]
We can rearrange this to solve for tension (T):
\[ T = v^2 \cdot \mu \]
Substituting the values we found:
\[ T = (40 \text{ m/s})^2 \cdot 0.05 \text{ kg/m} = 1600 \cdot 0.05 = 80 \text{ N} \]

### Conclusion:
The tension in the cord is **80 N**.

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