The weight of a body is usually meaasured by disregarding bo

The weight of a body is usually meaasured by disregarding bouyancy force applied by the air. Consider a 20-cm-diameter spherical body of density 7800 kg/m^3. What is the percentage error associated with the neglecting of air bouyancy?

Solution

We know that the buoyant for a body acts on it vertically up and is given by the weight of the fluid displaced by the body.

So as to determine the percentage error associated with neglecting the air bouyancy, we will need to calculate by what amount does the buoyancy would reduce the weight of the body and then find this value as the percentage of the actual weight of the body.

Now the buoyant force acting on a volume v in fluid with density d is given as Vd

Hence the buoyant force acting on the body given is (4/3)R^3d = 4 x 3.14 x 10^-3 x 1.225 / 3 [density of air = 1.225 Kg / m^3]

or, F_B =  5.12867 x 10^-3 N

Hence the actual weight of the body that acts downwards = Mg - F_B

Or, W =  (4/3) x 3.14 x 10^-3 x 7800 - Fb = 32.656 -  0.0051287 = 32.6508713 N

Therefore the percentage error due neglecting of buoyant force = 0.0051287 x 100 / 32.6508713 = 0.01571 %