Sure, let's tackle this problem step by step.
### (i) Definition of Relative Density
Relative density (also known as specific gravity) is a dimensionless quantity that is defined as the ratio of the density of a substance to the density of a reference substance. For most purposes, the reference substance is water. So, relative density can be expressed mathematically as:
[tex]\[ \text{Relative Density} = \frac{\text{Density of the substance}}{\text{Density of water}} \][/tex]
### (ii) Determining the Relative Density of Kerosene
We have the following information:
1. Weight of the stone in air: 3.6 N
2. Weight of the stone in water: 2.6 N
3. Weight of the stone in kerosene: 1.6 N
#### Step-by-Step Solution:
1. Calculate the buoyant force in water:
The buoyant force experienced by the stone when immersed in water can be found by the difference in weight of the stone in air and in water.
[tex]\[ \text{Buoyant Force in Water} = \text{Weight in Air} - \text{Weight in Water} \][/tex]
Substituting the given values:
[tex]\[ \text{Buoyant Force in Water} = 3.6 \text{ N} - 2.6 \text{ N} = 1.0 \text{ N} \][/tex]
2. Calculate the buoyant force in kerosene:
Similarly, the buoyant force in kerosene can be found by the difference in weight of the stone in air and in kerosene.
[tex]\[ \text{Buoyant Force in Kerosene} = \text{Weight in Air} - \text{Weight in Kerosene} \][/tex]
Substituting the given values:
[tex]\[ \text{Buoyant Force in Kerosene} = 3.6 \text{ N} - 1.6 \text{ N} = 2.0 \text{ N} \][/tex]
3. Determine the relative density of the kerosene:
The relative density of the kerosene can be found by dividing the buoyant force in kerosene by the buoyant force in water.
[tex]\[ \text{Relative Density of Kerosene} = \frac{\text{Buoyant Force in Kerosene}}{\text{Buoyant Force in Water}} \][/tex]
Substituting the calculated values:
[tex]\[ \text{Relative Density of Kerosene} = \frac{2.0 \text{ N}}{1.0 \text{ N}} = 2.0 \][/tex]
So, the relative density of kerosene is 2.0.
