an object of mass m and density d is surrounded by air of density p. show that the resultant force F acting...?

[kindelbow047]

an object of mass m and density d is surrounded by air of density p. show that the resultant force F acting downward on the object is given by F=mg[1-(p/d)]

Thank you in advance!!!

[Dr Zorro]

The object has volume V = m/d. Therefore it experiences a buoyant force (equal to the weight of the air displaced)

Fb = V p g = m p/d g

The net downward force therefore is

Fnet = m g - m p/d g = m g ( 1 - p/d)