Three masses of 2 kg each are hanging on a string passing over a fixed frictionless pulley as shown in the following figure. The value of tension in the string joining the masses B and C is

To determine the tension in the string connecting masses B and C, we first need to analyze the forces acting on each mass. Since all three masses are equal and hanging vertically, we can apply Newton's second law of motion to each mass to find the tension in the string.

Understanding the System

In this scenario, we have three masses (A, B, and C), each weighing 2 kg. The setup involves a fixed frictionless pulley, which means that the only forces acting on the masses are their weights and the tension in the strings. The weight of each mass can be calculated using the formula:

• Weight (W) = mass (m) × gravitational acceleration (g)

Assuming the gravitational acceleration (g) is approximately 9.81 m/s², the weight of each mass is:

• W = 2 kg × 9.81 m/s² = 19.62 N

Analyzing Mass B and Mass C

Masses B and C are hanging on either side of the string, and they will experience the same tension (T) in the string connecting them. Since they are in equilibrium (not accelerating), the forces acting on them must balance out. For mass B, the forces can be expressed as:

• Weight of B (downward) = Tension in the string (upward)

Thus, we can write the equation for mass B as:

• 19.62 N (weight of B) = T

This means that the tension in the string between masses B and C is equal to the weight of mass B, which is 19.62 N.

Considering Mass A

Mass A is also hanging and will affect the overall tension in the system. However, since we are specifically looking for the tension between B and C, we can conclude that the tension remains the same due to the equilibrium condition. If mass A were to be considered, we would analyze it separately, but it does not change the tension between B and C directly.

Final Thoughts

In summary, the tension in the string connecting masses B and C is equal to the weight of either mass, which is:

• T = 19.62 N

This analysis shows how the forces balance out in a system of hanging masses, allowing us to find the tension in the string effectively. If you have any further questions or need clarification on any part of this explanation, feel free to ask!