Why is an object's density expressed as a relationship between two units

Why do some things float and others sink? The first thing that comes to mind for many people is that it depends on how heavy an object is. While an object's weight*, or more properly its mass** does play a role, it is not the only factor. If it were, we could not explain how a giant ocean liner floats while a small pebble sinks. Mass matters, but there is more to it.

The ability of an object to float is described as its buoyancy. The buoyancy of an object is its tendency to float on or rise in a liquid. An object that floats in water is said to be positively buoyant. An object that sinks is negatively buoyant. To determine an object's buoyancy, both its mass and volume* must be taken into consideration. The relationship between object's volume and mass is called its density*. Density is defined as the mass of an object per unit volume. Mathematically, this relationship is described using the following equation

density = mass / volume

The standard metric unit for density is grams per cubic centimeter (g/cm3).

In order to explain how an object's density influences its buoyancy, the behavior of an object placed in water must be understood. When an object is placed in water, even a floating object displaces some of that water. The amount of water displaced is a function of the object's mass. The object sinks into the water until it displaces an amount of water equal to its own mass. A 1 g object will sink until it displaces 1 g of water. This is independent of its size or shape. Since water has a density of 1 g/cm3, a 1 g object will displace 1 cm3 of water.

the 2nd option is the answer