A uniform wooden plank floats in a swimming pool. The plank weighs 100 pounds, and exactly 10% of its volume is above the waterline. The maximum weight of iron which could be suspended from underneath the plank without causing the whole combination to sink to the bottom of the pool is
A) exactly 10 pounds.
B) somewhat more than 10 pounds.
C) somewhat less than 10 pounds.
D) more information is needed.

Question

Quizplus · Accepted Answer

The plank displaces water equal to its own weight (100 pounds) when floating. Since only 10% of the plank is above water, it means 90% of its volume is used to displace this weight in water. If iron is added, it will increase the weight without significantly changing the volume, allowing the plank to displace more water up to its maximum buoyant capacity. Therefore, the maximum weight of iron that can be added is somewhat more than 10 pounds, as this would utilize the remaining buoyant capacity of the plank without exceeding it.

A Uniform Wooden Plank Floats in a Swimming Pool