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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

Options

  1. AMg
  2. BMg - Vρg
  3. CMg + πR 2 hρg
  4. Dρg V + πR 2 h

Correct answer

D. ρg V + πR 2 h

Step-by-step solution

Net pressure force = weight of liquid displaced ⇒ F - ρghπR 2 = ρgV ⇒ F = ρg V + πR 2 h

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