A body weight 0.3N in air,0.25N when fully immersed in water and 0.27N when fully immersed in liquid. calculate a. It's water weight loss. b. It's relative density c.its relative density of the liquid.
a. 0.3 N - 0.25 N = L
b. .03 N / L
c. (0.3 N - 0.27 N) / (0.3 N - 0.25 N)
0.30
a. To calculate the weight loss in water, we subtract the weight of the body when fully immersed in water from its weight in air:
Weight loss in water = Weight in air - Weight in water
Weight loss in water = 0.3N - 0.25N = 0.05N
b. To calculate the relative density of the body, we divide its weight loss in water by the weight loss of an equal volume of water:
Relative density = Weight loss in water / Weight loss of water
Relative density = 0.05N / 0.25N = 0.2
c. To calculate the relative density of the liquid, we divide the weight loss in water by the weight loss in the liquid:
Relative density of the liquid = Weight loss in water / Weight loss in the liquid
Relative density of the liquid = 0.05N / (0.3N - 0.27N) = 0.05N / 0.03N = 1.67
So, a. the water weight loss is 0.05N, b. the relative density of the body is 0.2, and c. the relative density of the liquid is 1.67.
To calculate the information requested, we can use the following formulas:
a. Water weight loss = Weight in air - Weight in water
b. Relative density = Weight in air / (Weight in air - Weight in water)
c. Relative density of the liquid = Weight in air / (Weight in air - Weight in liquid)
Given values:
Weight in air = 0.3 N
Weight in water = 0.25 N
Weight in liquid = 0.27 N
Let's calculate the values step by step:
a. Water weight loss = Weight in air - Weight in water
= 0.3 N - 0.25 N
= 0.05 N
b. Relative density = Weight in air / (Weight in air - Weight in water)
= 0.3 N / (0.3 N - 0.25 N)
= 0.3 N / 0.05 N
= 6
c. Relative density of the liquid = Weight in air / (Weight in air - Weight in liquid)
= 0.3 N / (0.3 N - 0.27 N)
= 0.3 N / 0.03 N
= 10
Therefore:
a. The water weight loss is 0.05 N.
b. The relative density is 6.
c. The relative density of the liquid is 10.
To solve these calculations, we need to understand the concept of buoyancy and Archimedes' principle.
a. Water weight loss:
The weight loss in water is equal to the weight of the water displaced by the body. According to Archimedes' principle, the buoyant force experienced by an object immersed in a fluid is equal to the weight of the fluid displaced by the object.
The weight of the body in water is 0.25N, and its weight in air is 0.3N. Therefore, the weight loss in water can be calculated as the difference between these two weights:
Water weight loss = Weight in air - Weight in water
= 0.3N - 0.25N
= 0.05N
Therefore, the water weight loss of the body is 0.05N.
b. Relative density of the body:
Relative density, also known as specific gravity, compares the density of a substance to the density of another substance (usually water). Mathematically, it is defined as the ratio of the density of the substance to the density of water.
Relative density = Density of the body / Density of water
The density can be calculated using the weight and volume of the body:
Density = Mass / Volume
Since the weight of the body is given in this case, we need to convert it into mass using the acceleration due to gravity (e.g., 9.8 m/s^2 for Earth's gravity).
Mass = Weight / Acceleration due to gravity
The mass in air can be calculated as follows:
Mass in air = Weight in air / Acceleration due to gravity
= 0.3N / 9.8 m/s^2
≈ 0.031 kg
The mass in water can be calculated in the same way:
Mass in water = Weight in water / Acceleration due to gravity
= 0.25N / 9.8 m/s^2
≈ 0.026 kg
Now, we can calculate the relative density of the body:
Relative density of the body = Density of the body / Density of water
= (Mass in air / Volume) / (Mass in water / Volume)
= (Mass in air / Mass in water)
= 0.031 kg / 0.026 kg
≈ 1.19
Therefore, the relative density of the body is approximately 1.19.
c. Relative density of the liquid:
Similarly, the relative density of the liquid can be calculated using the weight of the body in the liquid.
Relative density of the liquid = (Weight in air - Weight in liquid) / (Weight in water - Weight in air)
Weight in liquid = 0.27N (as given)
Relative density of the liquid = (0.3N - 0.27N) / (0.25N - 0.3N)
Simplifying this equation gives:
Relative density of the liquid = 0.03N / -0.05N
≈ -0.6
Therefore, the relative density of the liquid is approximately -0.6.