Question

The volume of 50g of a substance is $20c{m^3}$. If the density of water is $1gc{m^{ - 3}}$, will the substance float or sink in water?

Answer 1

The given substance will float on water if the density of that substance is less than the given density of water and the substance will sink if its density is found to be more than the density of water. We can calculate the density of the substance as density is given by mass per unit volume of that substance.

Formula used: In the solution to this question, we will be using the following formula,
$\Rightarrow \rho = \dfrac{m}{V}$
where $\rho$ is the density of any substance and $m$ is the mass of the substance and $V$ is its volume.

Complete step by step answer:
The condition whether a body will float or sink in water is determined by the density of that substance. Here we are given the density of water $1gc{m^{ - 3}}$.
Now if the density of the given substance is more than the density of water then that substance will sink in water. But if we see that the density of the substance is less than the density of water then we can conclude that the body will float on the surface of the water.
Here we are given that 50g of that substance occupies $20c{m^3}$ of volume.
So from the given values, we can calculate the density as,
$\Rightarrow \rho = \dfrac{m}{V}$
Substituting the values of mass and volume we get,
$\Rightarrow \rho = \dfrac{{50}}{{20}}gc{m^{ - 3}}$
So on doing the above calculation we get the density as,
$\Rightarrow \rho = 2.5gc{m^{ - 3}}$
Therefore the density of this substance is more than the given density of water.
So from the previous explanation, we can conclude that the substance will sink in water as its density is greater than the density of water.

Note:
We can also solve this by the law of flotation, where a body floats on the surface of the water if the water displaces weights at least equal to the weight of the body. If the displaced water weighs less than the body then the body sinks.