A ball has a diameter of 3.84 cm and average density of 0.0841 g/cm3. What force is required to hold it completely submerged under water?

The force required to hold the ball completely submerged under water = 0.0273 N

Explanation:

Archimedes' principle theorizes that the weight of an object floating in a liquid is equal to the weight of the fluid displaced by the object. And the maximum amount of fluid that an object can displace is equal to the volume of the object. Thus an object would float only if density of the object is less than or equal to the density of the fluid.

If an object is having greater density than the liquid, then its weight would be greater than the weight of the fluid and would sink and in the fluid and move with a non zero acceleration.

The net upward force acting on the the body especially in a case where the body has a density lower than the fluid is

F = Fb - W₆ₐₗₗ

Fb = buoyant force of the liquid in the body = ρVg, ⁻⁰¹²³⁴⁵⁶⁷⁸⁹π

ρ = density of fluid = 1000 kg/m³

V = volume of ball = (4/3)πr³, r = D/2 = 3.84/2 = 1.92 cm = 0.0192 m

V = (4/3)π(0.0192)³ = 0.0000297 m³

g = acceleration due to gravity

W = weight of ball = ρ₆ₐₗₗVg

ρ₆ₐₗₗ = density of ball = 0.0841 g/cm³ = 8.41 kg/m³

Fb = 1000 × (0.0000297) × 9.8 = 0.0297 N

W = 8.41 × 0.0000297 × 9.8 = 0.00244 N

F = Fb - W = 0.0297 - 0.00244 = 0.0273 N

The force required to hold the ball completely submerged under water must at least nalance this net upaward force, hence, is = 0.0273 N