Question

A tank is filled with x kg water. If the water is replaced with y kg mercury. Find the ratio of x and y. (density of mercury = 13.6×10³ kg/m³)
1. 1 : 1.36
2. 1.36 : 1
3. 13.6 : 1
4. 1 : 13.6

Answer 1

Correct Answer - Option 4 : 1 : 13.6

CONCEPT:

Density

• The ratio of mass to volume of the body is known as the density of the material of the body.

\(⇒ ρ=\frac{m}{V}\)

Where ρ = density, m = mass and V = volume

CALCULATION:

Given m_w = x kg, m_Hg = y kg, ρ_Hg = 13.6×103 kg/m3 and ρ_w = 103 kg/m3

• The water in the tank is replaced with mercury so the volume of the water and the mercury will be the same.
• Let V is the volume of water.

The density is given as,

\(⇒ ρ=\frac{m}{V}\)     -----(1)

For water,

⇒ x = ρw × V

⇒ x = 10³ × V     -----(2)

For mercury,

⇒ y = ρ_Hg × V

⇒ y = 13.6 × 103 × V     -----(3)

By dividing equation 2 and equation 3,

\(\Rightarrow \frac{x}{y}=\frac{1}{13.6}\)

• Hence, option 4 is correct.