im stuck up with the following prob

consider 2 pulleys kept at the edges of a horizontal table to the right of the right edge a mass of 10kg is hung thro a string passing over a pulley attached to one end of a spring balance kept horizontally(not touching the ground)to the other a mass of 5kg(hanging on the other edge) is connected thro a string passing over the other pulley.FIND THE READING ON THE SPRING BALANCE.

plz help me with this .

To solve this problem, we need to analyze the forces acting on the system involving the two masses and the spring balance. Let's break it down step by step.

Understanding the Setup

We have two masses: a 10 kg mass hanging on one side and a 5 kg mass hanging on the other side, both connected by a string that passes over two pulleys. The spring balance is positioned horizontally and measures the tension in the string. Since the system is in equilibrium, we can determine the reading on the spring balance by analyzing the forces involved.

Identifying Forces

First, let's identify the forces acting on each mass:

• The force acting on the 10 kg mass (Weight = m × g) is:
• Weight of 10 kg = 10 kg × 9.81 m/s² = 98.1 N
• The force acting on the 5 kg mass is:
• Weight of 5 kg = 5 kg × 9.81 m/s² = 49.05 N

Analyzing the System

In this scenario, the 10 kg mass is heavier than the 5 kg mass. Therefore, it will exert a greater force downward, causing the system to accelerate. However, the spring balance measures the tension in the string, which is influenced by both masses.

Calculating Tension

To find the tension in the string, we can use the following approach:

• Let T be the tension in the string.
• For the 10 kg mass, the net force acting on it can be expressed as:
• Net force = Weight of 10 kg - T = 10 kg × a
• For the 5 kg mass, the net force is:
• Net force = T - Weight of 5 kg = 5 kg × a

Setting Up the Equations

Now we have two equations:

• 1. 98.1 N - T = 10a
• 2. T - 49.05 N = 5a

Solving the Equations

We can solve these equations simultaneously. From the second equation, we can express T in terms of a:

• T = 49.05 N + 5a

Substituting this expression for T into the first equation gives:

• 98.1 N - (49.05 N + 5a) = 10a

Now, simplifying this:

• 98.1 N - 49.05 N - 5a = 10a
• 49.05 N = 15a
• a = 49.05 N / 15 = 3.27 m/s²

Finding Tension Again

Now that we have the acceleration, we can find the tension T:

• T = 49.05 N + 5(3.27 m/s²) = 49.05 N + 16.35 N = 65.4 N

Final Reading on the Spring Balance

The reading on the spring balance, which measures the tension in the string, will be 65.4 N. This is the force that the spring balance will display as it balances the forces acting on the system.

In summary, the reading on the spring balance is 65.4 N, which reflects the tension created by the difference in weights of the two masses. If you have any further questions or need clarification on any part of this explanation, feel free to ask!