7 h2 hi P2 Calculate the weight in N of the sphere that is i

7 h2 hi P2 Calculate the weight (in N) of the sphere that is in equilibrium in the position shown: diameter = 0.05 m density11,004 kgm-3 density2 768 kgm-3 h1 = 13 cm h2 = 10 cm!

Solution

vertical downward force on upper half of sphere due to density2 liquid F2= density of fluid2* weight                                  of fluid resting on upper surface

F2= ₂g* (volume of fluid 2 above sphere – volume of half sphere)

            F2= ₂g* (d²h_2-d³/12)         

vertical upward force on bottom half of sphere due to density1 liquid F1= density of fluid 1* weight                                  of fluid resting on bottom surface

F1= ₁g* (volume of fluid 1 above sphere + volume of half sphere)

            F1= ₁g* (d²h₁ d+³/12)

By force equilibrium               F2+ weight = F1

                                             ₂g* (d²h_2-d³/12) + w = ₁g* (d²h₁₊d³/12)

                                                w= ₁g* (d²h₁₊d³/12) -         ₂g* (d²h_2-d³/12)

                                                w= ( ₁h1- ₂h2)gd²+ d³/6

                                    put values

                                                w= (1004*0.13-768*0.10)*9.81*0.05² +*0.05³/6

                                                w= 1.317483+ 0.000065

                                                w= 1.3175 N