Problem Statement:
A weight Mg is suspended from the middle of a rope whose ends are at the same level. The rope is no longer horizontal. What minimum tension is required to straighten it completely?

Solution:

Introduction:
In this problem, a weight Mg is suspended from the middle of a rope whose ends are at the same level. The rope is not horizontal, and we need to find the minimum tension required to completely straighten it.

Analysis:
To solve this problem, let's consider the forces acting on the weight Mg when the rope is not horizontal.

1. Weight of the object: The weight of the object acts vertically downwards and is equal to Mg, where M is the mass of the object and g is the acceleration due to gravity.

2. Tension in the rope: The tension in the rope acts in the direction of the rope and is denoted by T. As the rope is not horizontal, the tension can be divided into two components:
- Horizontal component: The horizontal component of the tension is Tcosθ, where θ is the angle between the rope and the horizontal.
- Vertical component: The vertical component of the tension is Tsinθ.

Minimum Tension to Straighten the Rope:
To completely straighten the rope, the vertical component of the tension should balance the weight of the object. This means that Tsinθ should be equal to Mg.

So, to find the minimum tension required to straighten the rope completely, we need to find the value of T.

Calculation:
From the above analysis, we have Tsinθ = Mg.

Dividing both sides by sinθ, we get T = Mg/sinθ.

Since sinθ is always less than or equal to 1, the minimum tension required to straighten the rope completely is Mg/sinθ.

Answer:
The minimum tension required to straighten the rope completely is Mg/sinθ.

Summary:
In this problem, we analyzed the forces acting on the weight Mg when the rope is not horizontal. We found that the minimum tension required to straighten the rope completely is Mg/sinθ.

4) infinitely large