Physics
Fluid-Mechanics
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text  A cylindrical vessel of radius  end text straight R text  and height  end text straight H text  has a liquid of density  end text rho text  upto a height  end text left parenthesis H much greater-than h right parenthesis text  .  end text
I f space t h e space c y l i n d e r space r o t a t e s space w i t h space a n space a n g u l a r space v e l o c i t y space space space a b o u t space t h e space v e r t i c a l space a x i s space d i f f e r e n c e space o f space t h e space l i q u i d space
l e v e l s space a t space t h e space p e r i p h e r y space w i l l space b e

  1. fraction numerator R squared omega over denominator 2 g end fraction
  2. fraction numerator R squared omega squared over denominator g end fraction
  3. fraction numerator R squared omega squared over denominator 2 g end fraction
  4. fraction numerator R squared omega over denominator g end fraction

The correct answer is: fraction numerator R squared omega squared over denominator 2 g end fraction


    table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell integral subscript 0 superscript h   h left parenthesis d F right parenthesis equals integral subscript 0 superscript h   y left parenthesis rho g y right parenthesis b left parenthesis d y right parenthesis equals rho g b integral subscript 0 superscript h   y squared left parenthesis d y right parenthesis equals fraction numerator rho g b h cubed over denominator 3 end fraction end cell row cell F equals F subscript 2 equals fraction numerator rho g b h squared over denominator 2 end fraction not stretchy rightwards double arrow r equals 1 over F integral y left parenthesis d F right parenthesis equals fraction numerator 2 h over denominator 3 end fraction end cell end table

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