A conical portion of radius R and height H is removed from the bottom of a cylinder of radius R . The volume of the remaining cylinder is V and its mass is M . It is suspended by a string in a liquid of density ρ where it stays vertical. The upper surface of the cylinder is at a depth h below the liquid surface. The force on the bottom of the cylinder by the liquid is

Question

A conical portion of radius R and height H is removed from the bottom of a cylinder of radius R . The volume of the remaining cylinder is V and its mass is M . It is suspended by a string in a liquid of density ρ where it stays vertical. The upper surface of the cylinder is at a depth h below the liquid surface. The force on the bottom of the cylinder by the liquid is <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-nxwzalfoor2c.png" /> (A) Mg (B) Mg-Vρg (C) Mg+π R2hρg (D) ρg(V + (π R)2 h)

Tardigrade Admin · Accepted Answer

Net pressure force = weight of liquid displaced ⇒ F-ρghπ R2=ρgV ⇒ F=ρg(V + π R2 h)

$M g$

$M g - V ρ g$

$M g + π R^{2} h ρ g$

$ρ g (V + (π R)^{2} h)$

Net pressure force = weight of liquid displaced
$\Rightarrow$ $F - ρ g hπ R^{2} = ρ g V$
$\Rightarrow$ $F = ρ g (V + π R^{2} h)$

Mg

Mg−Vρg

Mg+πR2hρg

ρg(V+(πR)2h)

Net pressure force = weight of liquid displaced ⇒ F−ρghπR2=ρgV ⇒ F=ρg(V+πR2h)

$M g$

$M g - V ρ g$

$M g + π R^{2} h ρ g$

$ρ g (V + (π R)^{2} h)$

Net pressure force = weight of liquid displaced
$\Rightarrow$ $F - ρ g hπ R^{2} = ρ g V$
$\Rightarrow$ $F = ρ g (V + π R^{2} h)$