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

Static equilibrium on the see-saw is achieved when the sum of moments around the fulcrum is zero. A moment is the product of force (weight) and its distance from the fulcrum.

Step 1: Box A weighs \( 50 \, \text{kg} \) and is \( 5 \, \text{m} \) from the fulcrum. Its moment is: \[ \text{Moment}_A = \text{Weight}_A \times \text{Distance}_A = 50 \times 5 = 250 \, \text{kg} \cdot \text{m} \]

Step 2: Let Box B's weight be \( W_B \). It is located \( 8 \, \text{m} \) from the fulcrum. Its moment is: \[ \text{Moment}_B = W_B \times 8 \]

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

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

Conclusion: Box B must weigh \( 31.25 \, \text{kg} \) for static equilibrium.