A solid weighs 20n in air and 12n in water determine the density of the solid
water weight displaced = 20 - 12 = 8 N
water mass displaced = 8 / 9.81 = 0.815 kg
water volume displaced =0.815 kg * ( 1 meter^3/1000 kg) = 0.000815 m^3
= volume of the solid
mass of solid = 20 /9.81 = 2.04 kg
so
density = mass/volume = 2.04 / .000815 = 2502 kg / m^3
or about 2.5 times the density of water
To determine the density of the solid, you can use the concept of buoyancy. The difference between the weight of the solid in air and the weight of the solid in water is equal to the buoyant force.
The weight of the solid in air is 20 N, and the weight of the solid in water is 12 N. We can use this information to find the buoyant force:
Buoyant force = Weight in air - Weight in water
Buoyant force = 20 N - 12 N
Buoyant force = 8 N
The buoyant force is equal to the weight of the water displaced by the solid. So, the volume of the water displaced can be found using Archimedes' principle:
Buoyant force = Weight of water displaced
density of water × volume of water displaced = Buoyant force
Since the density of water is known (approximately 1000 kg/m^3), we can rearrange the equation to solve for the volume of water displaced:
volume of water displaced = Buoyant force / density of water
volume of water displaced = 8 N / 1000 kg/m^3
volume of water displaced = 0.008 m^3
The density of the solid can now be determined using the formula:
Density = Mass / Volume
Since the mass is equal to the weight in air (20 N) divided by the acceleration due to gravity (approximately 9.8 m/s^2):
Mass = Weight in air / Acceleration due to gravity
Mass = 20 N / 9.8 m/s^2
Mass ≈ 2.04 kg
Density = Mass / Volume
Density = 2.04 kg / 0.008 m^3
Density ≈ 255 kg/m^3
Therefore, the density of the solid is approximately 255 kg/m^3.