A spherical vessel (diameter = 2.00 cm) when empty has a mass of 2.00 g. What is the greatest volume of water that can be placed in the vessel and still have the vessel float at the surface of water (Given: density of water = 1.00 g/cm³) A) 2.00 mL B) 31.5 mL C) 2.19 mL D) 4.19 mL E) the vessel will not float even when empty

Question

Quizplus · Accepted Answer

For a vessel to float, the buoyant force acting on it should be greater than or equal to the weight of the vessel. Buoyant force = weight of the fluid displaced by the vessel. Let's assume the height of the spherical vessel is h.

Volume of the spherical vessel = (4/3)πr^3 = (4/3)π(1 cm)^3 = (4/3)π cm^3
Radius of the spherical vessel = 1 cm
Diameter of the spherical vessel = 2 cm

Mass of the spherical vessel = 2.00 g
Weight of the spherical vessel = mg = 2.00 g × 9.81 m/s^2 = 0.0196 N

Let's assume the maximum volume of water the vessel can hold be V_max.

When the spherical vessel is floating, the weight of the vessel is balanced by the buoyant force acting on it.
buoyant force = weight of the fluid displaced by the vessel
ρ_water×V_max×g = weight of the vessel
1.00 g/cm^3 × V_max × 9.81 m/s^2 = 0.0196 N
V_max = 0.0196 N ÷ (1.00 g/cm^3 × 9.81 m/s^2) = 0.00200 m^3 = 2.00 cm^3

So the maximum volume of water the vessel can hold is 2.00 cm^3 or 2.00 mL. The correct answer is (C).

A Spherical Vessel (Diameter = 2