Question Detail

This problem uses the Principle of Moments. Since the ruler is supported at its center of gravity (50 cm mark), the ruler's own weight doesn't create any torque. We only care about the forces added to it. 1. Identify the Distances from the Pivot The pivot is at the 50 cm mark.

• End A is at 0 cm.
• Force 1 ($F_1$ = 4 N): Positioned 20 cm from End A.
  • $0 + 20 = \text{20 cm mark}$
  • Distance from pivot ($d_1$) = $50 - 20 = \mathbf{30\text{ cm}}$ (Left side)
• Force 2 ($F_2$): Positioned at End B.
  • End B is at 100 cm.
  • Distance from pivot ($d_2$) = $100 - 50 = \mathbf{50\text{ cm}}$ (Right side)

2. Apply the Principle of Moments For equilibrium: $$\text{Anticlockwise Moment} = \text{Clockwise Moment}$$ $$F_1 \times d_1 = F_2 \times d_2$$ 3. Calculation $$4\text{ N} \times 30\text{ cm} = F_2 \times 50\text{ cm}$$ $$120 = 50F_2$$ $$F_2 = \frac{120}{50}$$ $$F_2 = \mathbf{2.4\text{ N}}$$ Final Result The force that must be applied to end B to restore equilibrium is 2.4 N. Note: Since the distance from the pivot to End B ($50\text{ cm}$) is larger than the distance to the $4\text{ N}$ force ($30\text{ cm}$), you need less force at the end to balance the rule. This is the "lever effect"!