Question

What is the relative density of the object immersed in water?

Answer 1

Hint: Formula for relative density is :
Relative density $ = \dfrac{{density\ of\ object}}{{density\ of\ reference}}$
Like specific gravity is measured in reference to water.
Using the above relation of relative density we will solve the problem.

Complete solution:
Let’s define relative density first, and then we will come to the conclusion of the problem.
Relative density: it is the ratio of density of the object to the density of the reference material .Like we have an example specific gravity where the reference material is water generally. Specific gravity has no units because both the quantities are density thus cancels each other’s unit. Relative densities of aqueous solutions are dependent on the concentration of dissolved solutes.
When an object is immersed in water it follows the Archimedes principle, which states that : when a body is wholly or partially immersed in a liquid , it displaces the volume of the liquid which is equal to the mass of the object.
Therefore, relative density of the object immersed in the water has the below expression:
Relative density$ = \dfrac{{\dfrac{{{m_o}}}{{{v_o}}}}}{{\dfrac{{{m_w}}}{{{v_w}}}}}$
(density $ = \dfrac{{mass}}{{volume}}$ ,${m_o},{m_w},{v_o},{v_w}$ are the mass of object, mass of water ,volume of object ,volume of water respectively.)
For the object, half is in air and half is in water immersed therefore,
Relative density is equal to the ratio of the density of the object in air to the density of the water in which it is immersed.

Note:
When the relative density of an object is equal to 1 then the densities of both the materials are equal. If the relative density is less than 1 then the object will float ,if the relative density is greater than 1 then the object will sink in water.