Acylinder with radius 5.00 cm and length 20.0 cm is lowered into a tank of glucose, which has a density of 1,385 kg/m3. the cylinder is lowered in four stages:

a) zero submersion
b) half-submerged to a depth of 10.0 cm
c) fully submerged to a depth of 20.0 cm
d) fully submerged to a depth of 30.0 cm
e). what is the buoyant force on the cylinder at each stage?

A)  E₁ = 0 , B) E₂ = 1.07 10² N , C)  E₃ = 2.13 10⁴ N , D) E4 = 2.13 104 N

Explanation:

The thrust of a fluid on a body is equal to the weight of the liquid dislodged by the body

Let's calculate for each case

A) body not submerged.

The thrust is zero because there is no liquid displaced

       E₁ = 0

B)  Let's calculate the submerged volume L = 10.0 cm

      V = π r² L

      V = π 5.00² 10.0

      V₂ = 785.4 cm3 = 7.85.4 10⁻⁶ m

      E₂ = ρ g V²

      E₂ = 1,385 9.8 785.4 10-6

      E₂ = 1.07 10² N

C) submerged body L = 20.0

      V = π r² L

      V = π 5.00 2 20

      V₃ = 1,570 cm3 = 1570 10⁻⁶ m³

      E₃ = ρ g V

      E₃ = 1,385 9.8 1570 10⁻⁶

      E₃ = 2.13 10⁴ N

D)    The body volume is the maximum so the thrust does not change

      E4 = 2.13 104 N