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The problem involves a balance system with a weight of 4 hanging on the left and an unknown weight hanging on the right. The system is divided into equal units, and we need to determine the value of the weight on the right side that will restore balance.

### Step-by-step Solution:

1. **Lever Principle**: 
   The problem involves the principle of moments or torques, where the product of the weight and its distance from the pivot (center) must be the same on both sides for the system to be in equilibrium.

2. **Left Side**:
   The weight on the left side is 4, and it is located 2 units from the center (pivot).

   So, the torque (moment) on the left side is:
   \[
   \text{Left Torque} = 4 \times 2 = 8
   \]

3. **Right Side**:
   Let the unknown weight on the right be \( x \), and it is located 4 units from the pivot.

   The torque on the right side is:
   \[
   \text{Right Torque} = x \times 4
   \]

4. **Equilibrium Condition**:
   For the system to be in equilibrium, the torques on both sides must be equal:
   \[
   4 \times 2 = x \times 4
   \]
   Simplifying this:
   \[
   8 = 4x
   \]
   Solving for \( x \):
   \[
   x = \frac{8}{4} = 2
   \]

Thus, the weight on the right must be **2** to restore the balance.

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Do you want further details or have any questions?

Here are some related questions to expand on this topic:

1. How would the solution change if the weight on the left were moved to a different position?
2. What if the distance between the units was not equal?
3. Can you apply the same principle for rotational equilibrium in three dimensions?
4. How would you solve this problem if there were additional weights on either side?
5. What other real-world systems can be modeled using the principle of moments?

**Tip**: Remember, when dealing with balance or equilibrium problems, always focus on the torques (product of force and distance from the pivot).

If a weight of 4 is hung on the left side of the balance, how much should the weight on the right side be to restore equilibrium?

Discover how to solve a balance problem by applying the lever principle. Learn how to calculate the weight needed to restore equilibrium using torque and distance from the pivot. Suitable for students in Grades 6-8.

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