Tension in the strings in equilibrium:

When the mass M is tied up to the top of the two identical poles of height H using massless strings of equal length, the system reaches equilibrium. In this scenario, the tension in the strings can be determined by considering the forces acting on the mass.

Forces acting on the mass:

1. Weight: The mass M experiences a downward force due to its weight, which can be calculated using the equation F = mg, where g is the acceleration due to gravity.

2. Tension in the strings: The mass is tied to the poles using two strings of equal length. Each string exerts an upward force on the mass, known as tension.

Equilibrium condition:

For the system to be in equilibrium, the sum of all the forces acting on the mass must be zero. Therefore, we can write the equilibrium equation as:

Tension + Tension - Weight = 0

2 * Tension = Weight

Tension = Weight / 2

Tension in terms of the mass:

The weight of the mass can be calculated as the product of its mass (M) and the acceleration due to gravity (g). Therefore, we can rewrite the equation for tension as:

Tension = (M * g) / 2

Distance between the poles:

The distance between the poles does not affect the tension in the strings. The tension is determined solely by the weight of the mass and the acceleration due to gravity. Therefore, regardless of the distance between the poles, the tension in the strings will always be (M * g) / 2.

Explanation:

In this scenario, the mass M is in equilibrium when tied to the top of the two identical poles using equal-length strings. The tension in the strings can be determined by considering the forces acting on the mass, which include the weight of the mass and the tension in the strings. By applying the equilibrium condition, we find that the tension in each string is equal to half the weight of the mass. The distance between the poles does not affect the tension in the strings, which is solely determined by the weight of the mass and the acceleration due to gravity. Therefore, the tension in the strings will always be (M * g) / 2, regardless of the distance between the poles.