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Water is filled up to a height h in a be...

Water is filled up to a height `h` in a beaker of radiys `R` as shown in the figure. The density of water is `rho`, 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 on this section by water on the other side of this section has magnitude

A

`|2P_(0)Rh+piR^(2)rhogh-2RT|`

B

`|2P_(0)Rh+Rrhogh^(2)-2RT|`

C

`|P_(0)piR^(2)+Rrhogh^(2)-2RT|`

D

`|P_(0)piR^(2)+Rrhogh^(2)-2RT|`

Text Solution

Verified by Experts

The correct Answer is:
B
Pushing force `= ltpgt` (Area)
`= (((p_(0))+(p_(0)+rhogh))/(2))(2Rh)`
`= 2p_(0)Rh + rhogh^(2)R`
Pulling force `= (T)(2R)`
Net force `= |2p_(0)Rh + rhogh^(2)R - 2TR|`
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Knowledge Check

  • 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 -

    A
    `|2P_(0)Rh+piR^(2)rhogh-2RT|`
    B
    `|2P_(0)Rh+Rrhogh^(2)-2RT|`
    C
    `|P_(0)piR^(2)+Rrhogh^(2)-2RT|`
    D
    `|P_(0)piR^(2)+Rrhogh^(2)-2RT|`

  • Water rises upto a height h in a capillary tube of radius r. What is the network done in this process if the density of water is rho ?

    A
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    B
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    C
    `2pir^(2)hrhog`
    D
    `(pir^(2)grhog)/2`

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