If 50 pounds of weight is located at point X and 100 pounds at point Y, how much weight is needed at point Z to balance the plank?

• A. 25 pounds
• B. 50 pounds
• C. 75 pounds
• D. 100 pounds

Answer: (B)

To determine the amount of weight needed at point Z to balance the plank, we need to consider the concept of moments and how they create balance. The plank will be balanced if the moments (weight times distance from the pivot point) on one side are equal to the moments on the other side.

Assuming the distances of points X, Y, and Z from the pivot (fulcrum) of the plank are known, we would calculate the moments created by the weights at points X and Y.

For simplicity, let’s assume that points X and Y are equidistant from point Z, or that their distances are such that their combined effect can be balanced with a weight at point Z.

1. The moment created by the weight at point X can be calculated as: ( Moment_X = Weight_X \times Distance_X ).

2. The moment created by the weight at point Y can be calculated as: ( Moment_Y = Weight_Y \times Distance_Y ).

3. To balance the plank: ( Moment_Z = Weight_Z \times Distance_Z ).

The weight at Z must be such that the sum of moments on one side equals the sum of moments on the other side, leading to a state of equilibrium.

If we