Question

A rubber ball filled with air has a diameter of 25.0cm and an average density of 0.085s/cm^3. What force is required to hold the ball in equilibrium immediately below the surface of water in a swimming pool?

Answer 1

Archimedes' principle states that the buoyant force is equal to the weight of the water that is displaced.

The volume of a sphere is 4/3 * pi * r^3

4/3 * pi * 12.5^3 = 8181 cubic centimeters

Mass of ball = density*volume = 0.085 g/cm3 * 8181 = 0.695 kg

The mass of water is 1 gram / cubic centimeter

So the ball displaces 8181 grams of water

Since the ball's mass is 0.695 kg, subtract it from the mass of the water displaced, 8181- 695 = 7486 grams

7486 grams = 7.486 kg

F = ma

F = 7.486 kg * 9.8 m/sec^2

= 73.36 N