A uniformly tapering vessel of height h whose lower and upper radii are r and R is completely filled with a liquid of density ρ. The force that acts on the base of the vessel due to the liquid is

Question

A uniformly tapering vessel of height h whose lower and upper radii are r and R is completely filled with a liquid of density ρ. The force that acts on the base of the vessel due to the liquid is (A) π R2 h ρ g (B) π r2 h ρ g (C) π((R+r/2))2 h ρ g (D) (1/3) π(R2-r2) h ρ g

Tardigrade Admin · Accepted Answer

P at base =ρ g h F text Base =P text Base × A text Base =ρ g h × π r2=π r2 ρ g h

Q. A uniformly tapering vessel of height $h$ whose lower and upper radii are $r$ and $R$ is completely filled with a liquid of density $ρ$ . The force that acts on the base of the vessel due to the liquid is

$π R^{2} h ρ g$

$π r^{2} h ρ g$

$π (\frac{R + r}{2})^{2} h ρ g$

$\frac{1}{3} π (R^{2} - r^{2}) h ρ g$

$P$ at base $= ρ g h$
$F_{Base} = P_{Base} \times A_{Base} = ρ g h \times π r^{2} = π r^{2} ρ g h$

Q. A uniformly tapering vessel of height h whose lower and upper radii are r and R is completely filled with a liquid of density ρ. The force that acts on the base of the vessel due to the liquid is

πR2hρg

πr2hρg

π(2R+r​)2hρg

31​π(R2−r2)hρg