### Tension in a String Connected to Two Boxes**Problem Description:**Two boxes are connected to each other by a string in a system, as shown in the figure. The 10-N box slides without friction on a horizontal table surface. The pulley is ideal, and the string has negligible mass. The question is about determining the tension \( T \) in the string.**Hint:** You can solve this without needing to solve for the tension exactly.**Visual Representation:**In the provided figure:- The 10-N box rests on a horizontal table.- A string is connected to this 10-N box and goes over a pulley.- The other end of the string is connected to a 30-N weight, which hangs vertically off the table.### Possible Answers:1. \( T = 10 \, \text{N} \)2. \( T = 40 \, \text{N} \)3. \( T = 30 \, \text{N} \)4. \( T < 30 \, \text{N} \)5. \( T > 30 \, \text{N} \)### Explanation:Consider the forces acting on both boxes:1. **For the 30-N weight (hanging vertically):** - The force of gravity acting downward is 30 N. - The tension \( T \) in the string acts upward. If the system were at equilibrium, the tension \( T \) would equal the weight, i.e., 30 N. However, since the 30-N weight is causing the 10-N box to accelerate, the tension must be less than 30 N in order to account for the net force required to accelerate the system.2. **For the 10-N box (on the table):** - The tension \( T \) in the string pulls the box horizontally.### Conclusion:The tension \( T \) in the string is causing the 10-N box to accelerate horizontally, and the same tension is counteracting part of the 30-N weight's force. Therefore:\[ T < 30 \, \text{N} \]So, the correct answer is:- \( T < 30 \, \text{N} \)This setup allows students to understand the principles of tension in strings, forces in equilibrium, and the effects of acceleration in a frictionless environment.

In the given question, Weight of the block kept on a horizontal surface (w) = 10kg Mass of the block…

Two boxes are connected to each other by a string as shown in the figure. The 10-N box slides without friction on the horizontal table surface. The pulley is ideal and the string has negligible mass. What is true about the tension T in the string? (HINT you can solve this without needing to solve for the tension exactly)

Two boxes are connected to each other by a string as shown in the figure. The 10-N box slides without friction on the horizontal table surface. The pulley is ideal and the string has negligible mass. What is true about the tension T in the string? (HINT you can solve this without needing to solve for the tension exactly)

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Chapter1: Units, Trigonometry. And Vectors

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Centripetal Force

A particle, body, object or certain mass while travelling in a rotational path or semicircular path, experiences an inertia force. If that inertia force pulls the towards the inward of the imaginary circle in the rotation, it is termed as centripetal force.

Question

### Tension in a String Connected to Two Boxes

**Problem Description:**

Two boxes are connected to each other by a string in a system, as shown in the figure. The 10-N box slides without friction on a horizontal table surface. The pulley is ideal, and the string has negligible mass. The question is about determining the tension \( T \) in the string.

**Hint:** You can solve this without needing to solve for the tension exactly.

**Visual Representation:**

In the provided figure:

- The 10-N box rests on a horizontal table.
- A string is connected to this 10-N box and goes over a pulley.
- The other end of the string is connected to a 30-N weight, which hangs vertically off the table.

### Possible Answers:

1. \( T = 10 \, \text{N} \)
2. \( T = 40 \, \text{N} \)
3. \( T = 30 \, \text{N} \)
4. \( T < 30 \, \text{N} \)
5. \( T > 30 \, \text{N} \)

### Explanation:

Consider the forces acting on both boxes:

1. **For the 30-N weight (hanging vertically):**
- The force of gravity acting downward is 30 N.
- The tension \( T \) in the string acts upward.

If the system were at equilibrium, the tension \( T \) would equal the weight, i.e., 30 N. However, since the 30-N weight is causing the 10-N box to accelerate, the tension must be less than 30 N in order to account for the net force required to accelerate the system.

2. **For the 10-N box (on the table):**
- The tension \( T \) in the string pulls the box horizontally.

### Conclusion:

The tension \( T \) in the string is causing the 10-N box to accelerate horizontally, and the same tension is counteracting part of the 30-N weight's force. Therefore:

\[ T < 30 \, \text{N} \]

So, the correct answer is:
- \( T < 30 \, \text{N} \)

This setup allows students to understand the principles of tension in strings, forces in equilibrium, and the effects of acceleration in a frictionless environment.

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