A body weighs 20N in air and 15N in another liquid. If it's weighs18N in water, calculate the relative density of the liquid
density of water = 1000 kg/m^3
force up from water on body = 20 - 18 = 2 N
so if V = volume of body
V* 1000 kg/m^3 * g= 2 N
V = 2/1000 g
force up from fluid = 20 -15 = 5 N
V * rho * g = 5
rho = 5 (1000 g /2) /g = 2.5 * 1000 = 2.5 times density of water
To calculate the relative density of the liquid, we can use the formula:
Relative Density = (Weight in air - Weight in liquid) / (Weight in air - Weight in water)
Given:
Weight in air = 20N
Weight in liquid = 15N
Weight in water = 18N
We can substitute these values into the formula:
Relative Density = (20N - 15N) / (20N - 18N)
Simplifying:
Relative Density = 5N / 2N
Finally, dividing the two values:
Relative Density = 2.5
Therefore, the relative density of the liquid is 2.5.
To calculate the relative density of the liquid, we need to understand the concept of relative density. Relative density compares the density of a substance to the density of another substance, usually a reference substance.
In this case, we can use water as the reference substance since we are given the weight of the body in water. The relative density of a substance is equal to the density of the substance divided by the density of the reference substance.
To calculate the relative density, we need to determine the densities of the body and the reference substance (water in this case).
The weight of an object is given by the formula:
Weight = Mass × Acceleration due to gravity
Given that the weight of the body in air is 20N, we can equate this to the formula:
20N = Mass × Acceleration due to gravity
Similarly, for the weight of the body in the liquid other than water (let's call it liquid A):
15N = Mass × Acceleration due to gravity
And for the weight of the body in water:
18N = Mass × Acceleration due to gravity
We know that the acceleration due to gravity is constant, so we can cancel it out when comparing the weights:
Weight in air / Weight in liquid A = Weight in air / Weight in water
Substituting the given values:
20N / 15N = 20N / 18N
Now, we can solve for the relative density of the liquid (density of liquid A / density of water):
Relative density = (Weight in air / Weight in liquid A) × (Weight in water / Weight in air)
Simplifying the equation further:
Relative density = (20N / 15N) × (18N / 20N)
Relative density = (18/15)
Relative density = 1.2
Therefore, the relative density of the liquid is 1.2.