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Work, Energy and Power

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Physics Part I

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Physics

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12

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 ω. The force exerted by the liquid at the other end is

  • MLω squared over 2
  • fraction numerator ML squared straight omega over denominator 2 end fraction
  • MLω squared
  • fraction numerator ML squared straight omega squared over denominator 2 end fraction

A.

MLω squared over 2

Let the length of a small element of tube be dx. 
Mass of this element
          dm space equals space straight M over straight L dx


where M is mass of filled liquid and L is length of tube. 
Force on this element
      dF space equals space dm space cross times space xω squared
space space space space space integral subscript 0 superscript straight F dF space equals space straight M over straight L straight omega squared integral subscript 0 superscript straight L xdx
or space space space space space space straight F space equals space straight M over straight L straight omega squared open square brackets straight L squared over 2 close square brackets space equals space MLω squared over 2
or space space space space space space space straight F space equals space 1 half MLω squared

Let the length of a small element of tube be dx. 
Mass of this element
          dm space equals space straight M over straight L dx


where M is mass of filled liquid and L is length of tube. 
Force on this element
      dF space equals space dm space cross times space xω squared
space space space space space integral subscript 0 superscript straight F dF space equals space straight M over straight L straight omega squared integral subscript 0 superscript straight L xdx
or space space space space space space straight F space equals space straight M over straight L straight omega squared open square brackets straight L squared over 2 close square brackets space equals space MLω squared over 2
or space space space space space space space straight F space equals space 1 half MLω squared

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