A metal weighs 20N in air,12N in water and 14N in kerosene. Calculate the relative density of
i)the metal
Ii)the kerosene
To calculate the relative density of an object, we need to compare its density to the density of a reference substance. In this case, let's use water as the reference substance.
The weight of the metal in air is 20N.
The weight of the metal in water is 12N.
The weight of a substance is equal to its mass times the acceleration due to gravity. So we can write the following equations:
Weight in air = Mass x Acceleration due to gravity
20N = Mass x g
Weight in water = (Weight in air) - (Weight of displaced water)
12N = 20N - (Mass of displaced water) x g
A couple of notes before we proceed:
1) The density of water is 1000 kg/m^3.
2) The acceleration due to gravity (g) is approximately 9.8 m/s^2.
Now, let's solve these equations to find the mass of the metal:
20N = Mass x 9.8 m/s^2
Mass = 20N / 9.8 m/s^2 ≈ 2.04 kg
12N = 20N - (Mass of displaced water) x 9.8 m/s^2
Mass of displaced water = (20N - 12N) / 9.8 m/s^2 ≈ 0.82 kg
The relative density of the metal is equal to the ratio of its density to the density of water:
Relative Density of the metal = Density of metal / Density of water
Relative Density of the metal = (Mass of the metal) / (Volume of the metal) / (Density of water)
Relative Density of the metal = (2.04 kg) / (Volume of the metal) / (1000 kg/m^3)
Next, let's calculate the relative density of kerosene:
The weight of the metal in kerosene is 14N.
Weight in kerosene = (Weight in air) - (Weight of displaced kerosene)
14N = 20N - (Mass of displaced kerosene) x 9.8 m/s^2
Solving this equation, we find:
Mass of displaced kerosene = (20N - 14N) / 9.8 m/s^2 ≈ 0.61 kg
The relative density of kerosene can be calculated in the same way as the relative density of the metal:
Relative Density of kerosene = (Mass of the kerosene) / (Volume of the kerosene) / (Density of water)
Relative Density of kerosene = (0.61 kg) / (Volume of the kerosene) / (1000 kg/m^3)
To calculate the relative density of the metal and kerosene, we can use the formula:
Relative density = (Weight in air) / (Loss of weight in liquid)
For the metal:
i) Relative density of the metal = (Weight in air) / (Loss of weight in water)
= 20N / (20N - 12N)
= 20N / 8N
= 2.5
Therefore, the relative density of the metal is 2.5.
For the kerosene:
ii) Relative density of kerosene = (Weight in air)/(Loss of weight in kerosene)
= 20N / (20N - 14N)
= 20N / 6N
= 3.33 (rounded to two decimal places)
Therefore, the relative density of kerosene is 3.33.