In situation 2, if h2 is further decreased, then [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. In situation 2, if $h_{2}$ is further decreased, then [2006]

Smart Achievers · Accepted Answer

(1)

In situation - 2 when the height $h_{2}$ of water level is further decreased, then the upward force acting on the wooden block decreases. The total force downward remains the same. This difference will be compensated by the normal reaction by the tank wall on the wooden block. Hence the block does not moves up and remains at its original position.

Solution

1 cylinder will not move up and remains at its original position

2 for $h_{2} = \frac{h}{3}$ , cylinder again starts moving up

3 for $h_{2} = \frac{h}{4}$ , cylinder again starts moving up

4 for $h_{2} = \frac{h}{5}$ , cylinder again starts moving up

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Solution

1 cylinder will not move up and remains at its original position

2 for h2=h3, cylinder again starts moving up

3 for h2=h4, cylinder again starts moving up

4 for h2=h5, cylinder again starts moving up

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2 for $h_{2} = \frac{h}{3}$ , cylinder again starts moving up

3 for $h_{2} = \frac{h}{4}$ , cylinder again starts moving up

4 for $h_{2} = \frac{h}{5}$ , cylinder again starts moving up