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Physics

Fluid-Mechanics

Easy

Question

A wooden cylinder of diameter 4r, height h and density $rho over 3$ is kept on a hole of diameter 2r of tank, filled with liquid of density as shown in the figure.
Now level of the liquid starts decreasing slowly. When the level of liquid is at a height h₁above the cylinder the block starts moving up. At what value of h₁ will the block rise?

$\frac{4 h}{9}$
$\frac{5 h}{9}$
$\frac{5 h}{3}$
Remains same

The correct answer is: $fraction numerator 5 h over denominator 3 end fraction$

$text Let end text A subscript 1 equals text Area of cross-section of cylinder end text equals 4 pi r squared A subscript 2 equals text Area of base of cylinder in air end text equals pi squared text and end text A subscript 3 equals text Area of base of cylinder in water end text equals A subscript 1 minus A subscript 2 equals 3 pi r squared$
Drawing free body diagram of cylinder
$text Equating the net downward forces and net upward forces, we get, end text h subscript 1 equals 5 over 3 h$

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