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Paragraph: A wooden cylinder of diameter 4 r , height H and density / 3 is kept on a hole of diameter 2 r of a tank, filled with liquid of density as shown in the figure. Question: Now level of the liquid starts decreasing slowly. When the level of liquid is at a height h₁ above the cylinder, the block starts moving up. At what value of h₁ , will the block rise?

Options

  1. A4 h 9
  2. B5 h 9
  3. C5 h 3
  4. Dremains same

Correct answer

C. 5 h 3

Step-by-step solution

Let A₁= Area of cross-section of cylinder =4 r^2A₂= Area of base of cylinder in air = r^2 and A₃= Area of base of cylinder in water =A₁-A₂=3 r^2 Drawing free body diagram of cylinder. Equation the net downward forces and net upward forces, we get h₁= 5 3 H

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