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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 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.

A

`Momega^(2)L/2`

B

`Momega^(2)L`

C

`Momega^(2)L/4`

D

`Momega^(2)L^(2)/2`

Text Solution

Verified by Experts

The correct Answer is:
a
Mass of liquid in unit length `=M/L`
`therefore` Mass in element dx= `(Mdx)/L`
`therefore` Centripetal force `=(Mdx)/(L)xomega^(2)`
or `dF = (Momega^(2))/(L) x dx`
`therefore int dF = int_(0)^(L) (Momega^(2))/(L) xdx`
or `F=(Momega^(2))/(L) [x^(2)/2]_(0)^(L) = (ML^(2)omega^(2))/(2L)`or `F = (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 .

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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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