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A cylindrical tank has a hole of diamete...

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

Situation I: Initially, the tank is filled with water of density `rho` 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.
Find the minimum value of height `h_1` (in situation 1), for which the block just starts to move up?

A

`h//3`

B

`4h//9`

C

`2h//3`

D

`h`

Text Solution

Verified by Experts

The correct Answer is:
B
Again considering equilibrium of wooden block
Total downward force `=`Total upwards Wt. of block `+` force due to atmospheric pressure `=` Force due to pressure of liquid `+` Force due to atmospheric pressure
`pi(16r^(2))rho/3+g+P_(0)pixx16r^(2)`
`=[h_(2)rhog+p_(0)]pi[16-4r^(2)]+P_(0)xx4r^(2)`
`pi(16r^(2))hrho/g g=h_(2)rhogxxpix12r^(2)`
`16 h/3 =12h_(2)`
`impliesh_(2)=4/9h`
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