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A tube of length L is filled completely ...

A tube of length L is filled completely with an incompressible liquid of mass M and closed at both ends. The tube is then roted in a horizontal plane about one of its ends with a uniform angular velocity `omega` The force exerted by the liquid at the other end is

A

`(MLomega^(2))/(2)`

B

`MLomega^(2)`

C

`(MLomega^(2))/(4)`

D

`(ML^(2)omega^(2))/(2)`

Text Solution

Verified by Experts

(a) `dm=(M)/(L)dx`
`dF=(M)/(L) fx`
`dF=dmxomega_(0)`

`int_(0)^(f)dF=(M)/(L)omega^(2)int_(0)^(L)xdx`
`F=(M)/(L)omega^(2)(L^(2))/(2)=(MLomega^(2))/(2)`
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A tube of length L is filled completely with an incompressible liquid of mass M and closed at both ends . The tube is then rotated in a horizontal plane about one of its end with a uniform angular velocity omega . Find the force exerted by the liquid at the other end .

A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity omega . Determine the force exerted by the liquid at the other end.

Knowledge Check

  • A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity omega . The force exerted by the liquid at the other end is

    A
    `(Momega^(2)L)/2`
    B
    `Momega^(2)L`
    C
    `(Momega^(2)L)/4`
    D
    `(Momega^(2)L^(2))/2`

  • A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with, a uniform angular velocity co. The force exerted by the liquid at the other end is

    A
    `Momega^2l//2`
    B
    `Momega^2l`
    C
    `Momega^2l//4`
    D
    `Momega^2l^2//2`

  • A tube of length 'L' is filled completely with an in compressiblem liquid of mass 'M' and closed at both ends. The tube is then rotated in a horizontal plane about one of it's ends with a uniform angular velocity 'omega' . Then which of following statements are true :

    A
    The force exerted by liquid at the other end is `(1)/(2)M omega^(2)L`
    B
    Ratio of force at middle and point of the tube will be `4:1`
    C
    The force between liquid layers linearly with the distance along the lenghth of tube
    D
    Force is constant

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