Question 10: Finding Mass C (Corrected)
Step 1: Identify Torque Distances
From the diagram, we count the unit divisions from the fulcrum:
- Left Side:
- Mass \( m \) is at distance 3 units.
- Mass \( 3m \) is at distance 1 unit.
- Right Side:
- Mass \( m \) is at distance 4 units.
- Mass \( C \) is at distance 3 units.
Step 2: Balance Equation
Sum of Left Torques = Sum of Right Torques
$$ (m \cdot 3) + (3m \cdot 1) = (m \cdot 4) + (C \cdot 3) $$ $$ 3m + 3m = 4m + 3C $$ $$ 6m = 4m + 3C $$Step 3: Solve for C
$$ 2m = 3C $$
$$ C = \frac{2}{3}m $$
Substitute \( m = 6 \) kg:
$$ C = \frac{2}{3} \times 6 = 4 \text{ kg} $$
Answer: 4 kg