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JEE Advanced 2006
Exam
JEE Advanced
Year
2006
Subject
Physics
Chapter
Mechanical Properties of Fluids

JEE Advanced 2006 · Physics · Mechanical Properties of Fluids

Paragraph: A wooden cylinder of diameter 4 r , height H and density...

Paragraph: A wooden cylinder of diameter 4r4 r, height HH and density ρ/3\rho / 3 is kept on a hole of diameter 2r2 r of a tank, filled with liquid of density ρ\rho as shown in the figure.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,
Question: Now level of the liquid starts decreasing slowly. When the level of liquid is at a height h1h_1 above the cylinder, the block starts moving up. At what value of h1h_1, will the block rise?

Options

  1. A4h9\frac{4 h}{9}
  2. B5h9\frac{5 h}{9}
  3. C5h3\frac{5 h}{3}
  4. Dremains same

Correct answer

C. 5h3\frac{5 h}{3}

Step-by-step solution

Let A1=A_1= Area of cross-section of cylinder =4πr2A2==4 \pi r^2A_2= Area of base of cylinder in air =πr2=\pi r^2 and A3=A_3= Area of base of cylinder in water =A_1-A_2=3 π\pir^2 Drawing free body diagram of cylinder. Equation the net downward forces and net upward forces, we get h_1=53\frac{5}{3}H 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,
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