Question

Will the body sink in water or not if a body of mass $400g$ has a volume of $300c{m^3}$? It is given that the density of water is $1000kg/{m^3}$.
A. Sink
B. Float
C. Sink Partly
D. Float Partly

Answer 1

Find the density of body by the formula of density –
$\rho = \dfrac{m}{V}$
where, $m$ is the mass of the body and $V$ is the volume of the body.
Compare the density of water and body.

Complete step-by-step solution :
There are many uses of density but the very well - known application of density is that it is used to determine that the substance or an object will float on water or not. If the density of substance is less than the density of water it will float and if density of water is less than the density of that substance then that substance will sink.
Therefore, in the question –
Let the density of body be ${\rho _b}$ and density of water be ${\rho _w}$
According to the question, it is given that –
Mass of body, $m = 400g$ and
Volume of body, $V = 300c{m^3}$
Now, the density of body can be calculated by –
${\rho _b} = \dfrac{{400}}{{300}}g/c{m^3} \\\ {\rho _b} = 1.33g/c{m^3} \\\$
It is given that density of water, ${\rho _w} = 1000kg/{m^3}$
Converting the unit of density of water from $kg/{m^3}$ to $g/c{m^3}$, we get
${\rho _w} = 1g/c{m^3}$
Now, comparing the density of water and density of body, we get
${\rho _b} > {\rho _w}$
Density of the body is greater than the density of water.
As mentioned earlier, if the density of the body is greater than the density of water then, the body will sink.
Therefore, option (A) is the correct answer.

Note:- The mass per unit volume is called Density. In other words, we can say that it is the ratio of mass and volume of a body. Density is denoted by symbol called rho, $\rho .$ Therefore, mathematically we can represent density as –
$\rho = \dfrac{m}{V}$