Two persons are holding a rope of negligible weight tightly at its ends so that it is horizontal. A `15kg` weight is attached to rope at the midpoint which now no more remains horizontal The minimum tension required to completely straighten the rope is .

Options

A. `150N`
B. `75N`
C. `50N`
D. Infinitely large

Explanation

To solve the problem of determining the minimum tension required to completely straighten the rope when a 15 kg weight is attached to its midpoint, we can follow these steps:

### Step 1: Understand the Forces Acting on the System
When the 15 kg weight is attached to the midpoint of the rope, it creates a downward force due to gravity. The force can be calculated using the formula:
\[ F = m \cdot g \]
where:
- \( m = 15 \, \text{kg} \) (mass of the weight)
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)

### Step 2: Calculate the Weight Force
Substituting the values into the formula:
\[ F = 15 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 147 \, \text{N} \]
This is the force acting downwards due to the weight.

### Step 3: Analyze the Tension in the Rope
When the rope is held tightly at both ends, the tension in the rope must counteract the weight. If we denote the tension in the rope as \( T \), and since there are two segments of the rope supporting the weight, the vertical components of the tension must balance the weight:
\[ 2T \cdot \cos(\theta) = mg \]
Where \( \theta \) is the angle that the rope makes with the horizontal.

### Step 4: Determine the Condition for Straightening the Rope
To completely straighten the rope, the angle \( \theta \) must be such that the rope is horizontal. However, if the rope is horizontal, \( \cos(90^\circ) = 0 \), which means:
\[ 2T \cdot 0 = 147 \, \text{N} \]
This implies that the tension must be infinitely large to maintain a horizontal position, which is not physically possible.

### Step 5: Conclusion
Therefore, the minimum tension required to completely straighten the rope is theoretically infinite. This means that it is impossible to keep the rope horizontal while supporting the 15 kg weight at its midpoint.

### Final Answer
The minimum tension required to completely straighten the rope is infinite.

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