Question

The volume of mercury and water is $50\,ml$ each. What is the ratio of their mass, if their densities are in ratio 68:5?
A. 88:5
B. 68:5
C. 78:5
D. 58:5

Answer 1

Hint: In order to solve the question, we will first use the relationship between density, mass and volume to find the density of mercury and water and then we will divide both the densities after then we will substitute the value of ratio of densities in the divided equation to find the ratio of masses

Formula used:
$D = \dfrac{M}{V}$
Where, $D$ refers to density, $M$ refers to mass and $V$ refers to volume.

Complete step by step answer:
In the question we are given the volume of mercury and water the same and we are also given the ratio of their densities and we have to find the ratio of their mass.
Volume of mercury = 50 ml
Volume of water = 50 ml
Let the density of mercury = ${D_1}$
Let the density of water = ${D_2}$
Let the density of mercury = ${M_1}$
Let the density of water = ${M_2}$
ratio of densities = 68:5
$\dfrac{{{D_1}}}{{{D_2}}} = \dfrac{{68}}{5}$ ………………….. (equation 1)

Now we will apply the relation of density mass and volume of mercury
${D_1} = \dfrac{{{M_1}}}{V}$
Now we will substitute the value of volume of mercury in the above formula
${D_1} = \dfrac{{{M_1}}}{{50{\text{ ml}}}}$ ………………….. (equation 2)
Now we will apply the relation of density mass and volume of water
${D_1} = \dfrac{{{M_1}}}{V}$
Now we will substitute the value of volume of water in the above formula
${D_2} = \dfrac{{{M_2}}}{{50{\text{ ml}}}}$ ………………….. (equation 3)
Divide the equation 2 and equation 3
$\dfrac{{{D_1}}}{{{D_2}}} = \dfrac{{\dfrac{{{M_1}}}{{50{\text{ ml}}}}}}{{\dfrac{{{M_2}}}{{50{\text{ ml}}}}}}$ ………………….. (equation 4)
Now we substitute the equation 1 in equation 4
$\dfrac{{68}}{5} = \dfrac{{\dfrac{{{M_1}}}{{50{\text{ ml}}}}}}{{\dfrac{{{M_2}}}{{50{\text{ ml}}}}}}$
Now we will cancel the 50 ml
$\dfrac{{68}}{5} = \dfrac{{{M_1}}}{{{M_2}}}$
$\therefore {M_1}:{M_2} = 68:5$

Hence, the correct answer is B.

Note: Many students may confuse between density and weight as but density depends on pressure, temperature, mass and volume. But the weight depends on the mass of the object and change in gravity while gravity does not affect the density therefore both have a common variable mass but have other factors too.