Question

In order to achieve the static equilibrium of the see-saw about the fulcrum \( P \), shown in the figure, the weight of Box B should be _________ kg, if the weight of Box A is 50 kg.

 

• A. 50
• B. 31.25
• C. 80
• D. 61.25

Hint:

In problems involving static equilibrium, always ensure the sum of moments (force × distance) around the fulcrum is zero for balance.

Answer 1

The Correct Option is B

To achieve static equilibrium on the see-saw, the sum of the moments about the fulcrum must be zero. The moment is calculated as the product of the force (weight) and the distance from the fulcrum.

Step 1: The weight of Box A is \( 50 \, \text{kg} \), and it is located \( 5 \, \text{m} \) from the fulcrum. The moment caused by Box A is: \[ \text{Moment}_A = \text{Weight}_A \times \text{Distance}_A = 50 \times 5 = 250 \, \text{kg} \cdot \text{m} \]

Step 2: Let the weight of Box B be \( W_B \), and it is located \( 8 \, \text{m} \) from the fulcrum. The moment caused by Box B is: \[ \text{Moment}_B = W_B \times 8 \]

Step 3: For static equilibrium, the moments about the fulcrum must balance: \[ \text{Moment}_A = \text{Moment}_B \] \[ 250 = W_B \times 8 \]

Step 4: Solve for \( W_B \): \[ W_B = \frac{250}{8} = 31.25 \, \text{kg} \]

Conclusion: The weight of Box B should be \( 31.25 \, \text{kg} \) to achieve static equilibrium.