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A wooden cylinder of diameter 4 r, heigh...

A wooden cylinder of diameter 4 r, height H and density `rho//3` is kept on a hole of diameter 2 r of a tank, filled with water of density `rho` as shown in the

If level of liquid starts decreasing slowly, when the level of liquid is at a height `h_(1)` above the cylinder, the block just start moving up. Then the value of `h_(1)` is

A

`(2h)/(3)`

B

`(5h)/(4)`

C

`(5h)/(3)`

D

`(5h)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
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Comprehension-I A wooden cylinder of diameter 4r , height h and density rho//3 is kept on a hole of diameter 2r of a tank, filled with water of denstiy p as shown in the figure. The height of the base of cylinder from the base of tank is H. Let the cylinder is prevented from moving up, by applying a force and water level is furthere decreased. Then, height of water level ( h_(2) in figure) for which the cylinder remains in original position without application of force is

Comprehension-I A wooden cylinder of diameter 4r , height h and density rho//3 is kept on a hole of diameter 2r of a tank, filled with water of denstiy p as shown in the figure. The height of the base of cylinder from the base of tank is H. Water is filled up to height h in a beaker of radius R as shown in the figure. The density of water is p, the surface tension of water is T and the atmospheric pressure is P_(0) Consider a vertical section ABCD of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude -

Knowledge Check

  • A wooden cylinder of diameter 4 r, height H and density rho//3 is kept on a hole of diameter 2 r of a tank, filled with water of density rho as shown in the If height h_(2) of water level is further decreased, then

    A
    cylinder will not move up and remains at its original position
    B
    for `h_(2) =H//3` , cylinder again starts moving up
    C
    for `h_(2) =H//4` , cylinder again starts moving up
    D
    for `h_(2) =H//5` , cylinder again starts moving up

  • A wooden cylinder of diameter 4 r, height H and density rho//3 is kept on a hole of diameter 2 r of a tank, filled with water of density rho as shown in the The block in the above question is maintained by external means and the level of liquid is lowered. The height h_(2) when this external force reduces to zero is

    A
    `4 H//9`
    B
    `5 H//9`
    C
    remains same
    D
    `2 H//3`

  • A wooden cylindrical of diameter 4r, height h and density rho//3 is kept on a hole of diameter 2r of a tank , filled with water of density rho as shown in the figure . The height of the base of cylinder from the base of tank is H . Let the cylinder is prevented from moving up , by applying a force and water level is further decreased . Then , height of water level ( h_(2) in figure ) for which the cylinder remains in original position without application of force is

    A
    h/3
    B
    4h/9
    C
    2h/3
    D
    h

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