Question

A sample of metal weighs 210g in air, 140g in water and 120g in an unknown liquid. Then
A. The density of the metal is $3$${\text{g/c}}{{\text{m}}^{\text{3}}}$
B. The density of the metal is $7$${\text{g/c}}{{\text{m}}^{\text{3}}}$
C. Density of the sample metal is 4 times the density of unknown liquid
D. The metal still floats in water

Answer 1

Hint: To solve this question we need to use basic theory related to the relative density of the substance. As we know relative density is defined as the ratio of density of given substance to the density of a given reference material. As a sample of metal weighs given, we calculate the product of volume and density using the formula mentioned below and then after we divide equations as discussed below.

Formula used:- ${\text{density = }}\dfrac{{{\text{mass}}}}{{{\text{volume}}}}$

Complete Step-by-Step solution:
As given in question, Sample of metal weighs 210g in air, we have
We assume, density of material is ${\rho _{\text{m}}}$ and density of water is ${\rho _{\text{w}}}$.
Now, as we know,
Density is defined as the ratio of mass of sample to the volume of the given sample i.e.
${\text{density = }}\dfrac{{{\text{mass}}}}{{{\text{volume}}}}$
Apply this formula to get a calculated product of volume and density.
$V{\rho _m}{\text{g}}$ = 0.21g
$V{\rho _{\text{m}}}$=0.21 ………………………….…….. (I)
Here, we get the product of volume of the sample and density of material ${\rho _{\text{m}}}$.
It weighs 140g in water, we have
0.14g=0.21-$V{\rho _w}{\text{g}}$
$ \Rightarrow $0.14=0.21-$V{\rho _{\text{w}}}$
$ \Rightarrow $$V{\rho _w}$=0.07 …………………………. …….(II)
Dividing (I) by (II), we have
\[\dfrac{{{\rho _m}}}{{{\rho _w}}} = \dfrac{{0.21}}{{0.07}} = 3\]
${\rho _{\text{m}}}$=${\text{3}}{\rho _{\text{w}}}$
        = 3x1
       =3 $g/c{m^3}$
Thus, the density of the metal is 3 $g/c{m^3}$.
Therefore, option (A) is the correct answer.

Note- Density and Relative Density both are different terms as we discuss here. First, we talk about Density: it is the ratio between the mass and the volume of a body. While, on the other hand Relative density is the ratio between the density of an object (substance) and the density of some other reference object at some given temperature.