A metre rule is pivoted at its mid-point with a vertical force of 10N hanging from the distance 30cm from the…

1. Analyze the question

We are dealing with the Principle of Moments. A metre rule is balanced at its pivot (the mid-point). For the rule to remain horizontal, the clockwise moment must equal the anticlockwise moment.

• Pivot: Mid-point
• Force 1 ($F_1$): 10N at a distance ($d_1$) of 30cm from the pivot.
• Force 2 ($F_2$): 15N at an unknown distance ($d_2$) from the pivot.

2. Explain the concept

The Principle of Moments states that for a body in equilibrium, the sum of clockwise moments about a point is equal to the sum of anticlockwise moments about the same point.

The formula for a moment is:

3. Show the solution

To balance the ruler, we set the moment of the first force equal to the moment of the second force:

Given values:

• $F_1 = 10\text{N}$
• $d_1 = 30\text{cm}$
• $F_2 = 15\text{N}$
• $d_2 = ?$

Calculation:

Now, solve for $d_2$:

4. Identify the answer

Comparing our result to the given options, 20cm corresponds to option C.

5. Tip

When solving "balancing" problems, always ensure your units are consistent. Since the distance is given in cm, your answer will also be in cm. Also, remember that the "pivot" acts as the fulcrum—always measure your distances from that specific point, not from the ends of the rule!