Question

What is relative density? What is the relation between the densities of object and water when buoyancy force is equal to the weight of the object?

Answer 1

The upward force produced by a fluid against the weight of a partially or fully submerged item is known as buoyancy or upthrust. The weight of the overlying fluid causes pressure to rise with depth in a column of fluid. As a result, the pressure at the bottom of a fluid column is larger than at the top. In the same way, the pressure at the bottom of an item submerged in a fluid is larger than the pressure at the top.

Complete answer:
The ratio of a substance's density (mass per unit volume) to the density of a particular reference material is known as relative density or specific gravity. For liquids, the reference is almost always water at its densest temperature ($4\text{ }{}^\circ C$); for gases, the reference is air at room temperature ($20\text{ }{}^\circ C$). In scientific circles, the phrase "relative density" is frequently used.

The item is subjected to a net upward force as a result of the pressure differential. The amount of the force is proportional to the pressure difference, and is equal to the weight of the fluid that would otherwise fill the submerged volume of the item, i.e. the displaced fluid (as stated by Archimedes' principle).

If the relative density of a material is less than one, it is less dense than the reference; if it is more than one, it is denser. The densities are identical if the relative density is precisely 1; that is, equal volumes of the two substances have the same mass. A substance having a relative density (or specific gravity) less than 1 will float in water if the reference material is water. An ice cube, for example, with a relative density of 0.91 will float. A material sinks if its relative density is larger than one.

Note: An item whose average density is larger than the average density of the fluid in which it is immersed sinks. If the object's density is lower than the liquid's, the force can keep it floating. This can only happen in a non-inertial reference frame that possesses a gravitational field or is speeding owing to a force other than gravity, both of which define a "downward" direction.