When a uniform rope of mass 3 kg is kept in horizontal position and 60 N force acts on the rope in horizontal direction then tension at midpoint A is T. For the same rope kept in vertical position if 60 N vertically upward direction then tension at mid point A is 7,. Then (T/T) is force acts in (A) 0.5 (B) 1 (C) 1.2 (D) 2

To find the ratio of tensions at the midpoint \( T \) when the rope is in horizontal and vertical positions under the influence of a 60 N force, let's analyze the two scenarios separately.

### Scenario 1: Horizontal Position

1. **Mass of the rope:** \( m = 3 \, \text{kg} \)
2. **Force acting horizontally:** \( F = 60 \, \text{N} \)

In this case, the force \( F \) is uniformly distributed along the rope. The tension at the midpoint \( T_{\text{horizontal}} \) can be considered as \( T \) because the entire length of the rope experiences the same force due to uniform distribution.

### Scenario 2: Vertical Position

1. **Mass of the rope:** \( m = 3 \, \text{kg} \)
2. **Force acting vertically upward:** \( F = 60 \, \text{N} \)
3. **Gravitational force (weight) on the rope:** \( W = mg = 3 \times 9.8 = 29.4 \, \text{N} \)

When the rope is hanging vertically, the tension varies along the length of the rope. At the midpoint, the tension \( T_{\text{vertical}} \) is due to the force pulling upwards and the weight of half of the rope below the midpoint.

Let's denote the length of the rope as \( L \) (though the exact length is not necessary for this calculation). 

Since the rope is uniform, the weight of the rope below the midpoint is half of the total weight:
\[ W_{\text{half}} = \frac{W}{2} = \frac{29.4}{2} = 14.7 \, \text{N} \]

Thus, the total tension at the midpoint when the rope is vertical is:
\[ T_{\text{vertical}} = F + W_{\text{half}} = 60 + 14.7 = 74.7 \, \text{N} \]

### Ratio of Tensions

Given that the tension in the horizontal case is \( T_{\text{horizontal}} = T \) and the tension in the vertical case is \( T_{\text{vertical}} = 74.7 \, \text{N} \):

\[ \frac{T_{\text{horizontal}}}{T_{\text{vertical}}} = \frac{T}{74.7} \]

We need to determine which option matches the given ratio:
- (A) \( 0.5 \)
- (B) \( 1 \)
- (C) \( 1.2 \)
- (D) \( 2 \)

To find \( T \) from the horizontal scenario:

Since the rope is uniform and the force is uniformly distributed, the tension \( T \) at the midpoint for a horizontal rope experiencing a force \( F \) can be estimated using the fact that the total force is balanced along the rope's length, suggesting:
\[ T = F = 60 \, \text{N} \]

Now the ratio is:
\[ \frac{T}{74.7} = \frac{60}{74.7} \approx 0.8 \]

Since none of the options exactly match \( 0.8 \), let's consider if this was a conceptual misinterpretation or if we can use the given options more practically.

Given the question format and options, the closest practical answer would be to select from the provided choices. However, none of them exactly match \( 0.8 \).

Upon reviewing the options:

- (A) \( 0.5 \)
- (B) \( 1 \)
- (C) \( 1.2 \)
- (D) \( 2 \)

Since \( 0.8 \) is closest to none of these and re-evaluating the assumptions and given information to match options:

### Correct Analysis Conclusion:
None of the given options accurately match the calculated ratio of \( 0.8 \).

**Thus, there might be a typo or conceptual error in the provided options**. Let's double-check or reframe the question for clarity with the same data.

Would you like to ask more details or have any questions? Here are 5 questions you might consider next:

1. How to solve for tension in different shapes of ropes (e.g., looped or circular)?
2. What is the effect of rope elasticity on the tension calculations?
3. How to determine the tension in a non-uniform rope under force?
4. What if the angle of applied force changes for the rope?
5. How does friction impact the tension in a rope on a rough surface?

**Tip:** Always recheck the dimensions and units consistency in problems involving physical forces and masses for precise results.

Understand how to calculate tension in a uniform rope when positioned horizontally and vertically under the influence of a 60 N force. Explore the differences in tension due to force distribution and weight considerations. Suitable for high school physics students.

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