Find the height of the water level (in situation II), for which the block remains in its original position without the application of any external force. [2006]

Question

A cylindrical tank has a hole of diameter $2 r$ in its bottom. The hole is covered by a wooden cylindrical block of diameter $4 r$ , height $h$ and density $ρ / 3$ .

Situation I: Initially, the tank is filled with water of density $ρ$ to a height such that the height of water above the top of the block is $h_{1}$ (measured from the top of the block).

Situation II: The water is removed from the tank to a height $h_{2}$ (measured from the bottom of the block), as shown in the figure. The height $h_{2}$ is smaller than $h$ (height of the block) and thus the block is exposed to the atmosphere.

Q. Find the height of the water level $h_{2}$ (in situation II), for which the block remains in its original position without the application of any external force. [2006]

Smart Achievers · Accepted Answer

(2)

$Again considering equilibrium of wooden block.$

$Total downward force = total force upwards$

$Wt. of block + force due to atmospheric pressure = force due to pressure of liquid + Force due to atmospheric pressure$

$π (16 r^{2}) \frac{ρ}{3} \times g + P_{0} π \times 16 r^{2} = [h_{2} ρ g + P_{0}] π [(16 - 4) r^{2}] + P_{0} \times 4 r^{2}$

$where h_{2} = height of the water level in situation-2 for$ $which the block remains in its original position.$

$∴$ $h_{2} = \frac{4}{9} h$

Solution

1 $\frac{h}{3}$

2 $\frac{4 h}{9}$

3 $\frac{2 h}{3}$

4 $h$

Want Us to Email you About Special Offers & Updates?

Solution

1 h3

2 4h9

3 2h3

4 h

Want Us to Email you About Special Offers & Updates?

1 $\frac{h}{3}$

2 $\frac{4 h}{9}$

3 $\frac{2 h}{3}$

4 $h$