1. **Problem Statement:** We need to verify the principle of moments using a meter ruler balanced on a support point O with two weights suspended at distances $l_1$ and $l_2$ from O. The goal is to find the unknown weight by balancing moments. 2. **Principle of Moments:** The system is in equilibrium when the sum of clockwise moments equals the sum of anti-clockwise moments about the pivot point O. $$\text{Sum of clockwise moments} = \text{Sum of anti-clockwise moments}$$ 3. **Formula:** If $W_1$ is the known weight at distance $l_1$ on one side and $W_2$ is the unknown weight at distance $l_2$ on the other side, then: $$W_1 \times l_1 = W_2 \times l_2$$ 4. **Rearranging to find unknown weight $W_2$:** $$W_2 = \frac{W_1 \times l_1}{l_2}$$ 5. **Explanation:** The moment is the product of the force (weight) and its perpendicular distance from the pivot. Balancing moments means the torque produced by weights on both sides is equal, so the ruler stays horizontal. 6. **Example Calculation:** Suppose $W_1 = 50$ grams, $l_1 = 5$ cm, and $l_2 = 10$ cm. Then: $$W_2 = \frac{50 \times 5}{10} = \frac{250}{10} = 25 \text{ grams}$$ 7. **Interpretation:** The unknown weight $W_2$ is 25 grams to balance the meter ruler at the given distances. 8. **Summary:** By measuring distances and using the known weight, we can calculate the unknown weight using the principle of moments, ensuring equilibrium.