A solid vertical cylinder of cross-sectional area A A\,A and height h h\,h is fully submerged in a liquid of density ρ\rhoρ. The top face of the cylinder is at a depth d d\,d below the liquid surface, as shown in the diagram. The atmospheric pressure at the liquid surface is patmp_{\text{atm}}patm, and the acceleration due to gravity is ggg.
Which of the following correctly gives the absolute pressure at the bottom face of the cylinder, pbottomp_{\text{bottom}}pbottom, and the magnitude of the net upward force (upthrust), FupF_{\text{up}}Fup, exerted on the cylinder by the liquid?
pbottom=patm+ρg(d+h)p_{\text{bottom}} = p_{\text{atm}} + \rho g(d+h)pbottom=patm+ρg(d+h) and Fup=ρghAF_{\text{up}} = \rho g h AFup=ρghA
pbottom=ρg(d+h)p_{\text{bottom}} = \rho g(d+h)pbottom=ρg(d+h) and Fup=(patm+ρgh)AF_{\text{up}} = (p_{\text{atm}} + \rho g h) AFup=(patm+ρgh)A
pbottom=patm+ρgdp_{\text{bottom}} = p_{\text{atm}} + \rho g dpbottom=patm+ρgd and Fup=ρghAF_{\text{up}} = \rho g h AFup=ρghA
pbottom=patm+ρg(d+h)p_{\text{bottom}} = p_{\text{atm}} + \rho g(d+h)pbottom=patm+ρg(d+h) and Fup=(patm+ρgh)AF_{\text{up}} = (p_{\text{atm}} + \rho g h) AFup=(patm+ρgh)A