Please give solution of this question in detail.

And what is the tension in the lower wire ?

To determine the tension in the lower wire, we first need to understand the context of the problem. Typically, this involves a scenario where two wires are supporting a load, and we need to analyze the forces acting on them. Let’s break this down step by step.

Understanding the Setup

Imagine a situation where we have a mass hanging from two wires. The upper wire supports the weight of the mass, while the lower wire may also be under tension depending on the configuration. To find the tension in the lower wire, we need to consider the forces acting on the system.

Identifying Forces

In a typical scenario, the following forces are at play:

• Weight of the Mass (W): This is the force due to gravity acting downward, calculated as W = mg, where m is the mass and g is the acceleration due to gravity (approximately 9.81 m/s²).
• Tension in the Upper Wire (T1): This is the force exerted by the upper wire to support the weight.
• Tension in the Lower Wire (T2): This is the force exerted by the lower wire, which may also support part of the load depending on the angle and configuration.

Applying Equilibrium Conditions

For the system to be in equilibrium, the sum of the forces acting on it must equal zero. This can be expressed mathematically as:

ΣF = 0

For vertical forces, this means:

T1 - W - T2 = 0

From this equation, we can rearrange it to find the tension in the lower wire:

T2 = T1 - W

Calculating Tension

Let’s say we have a mass of 10 kg hanging from the wires. The weight (W) would be:

W = mg = 10 kg * 9.81 m/s² = 98.1 N

If the tension in the upper wire (T1) is known, for example, let’s assume T1 is 120 N. We can now substitute these values into our equation:

T2 = T1 - W = 120 N - 98.1 N = 21.9 N

Interpreting the Result

The tension in the lower wire (T2) is 21.9 N. This means that while the upper wire is primarily responsible for supporting the weight of the mass, the lower wire also bears some of the load, albeit less than the upper wire.

Conclusion

In summary, to find the tension in the lower wire, we analyzed the forces acting on the system, applied the equilibrium condition, and performed calculations based on the known values. This method can be applied to various scenarios involving tension in wires, ensuring a clear understanding of how forces interact in a system.