A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as…

A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is 5 cm and the angular speed of rotation is ω rad s-1. The difference in the height, h in cm of liquid at the Centre of vessel and at the sides of the vessel will be :

 

  1. 2ω225g
  2. 5ω22g
  3. 25ω22g
  4. 2ω25g

Solution

ρdrω2r=ρgdh

ω20Rr dr=g0hdh

ω2R22=gh

 h=ω2R22g=25ω22g cm.

Asked in: JEE Main 2020 (02 Sep Shift 1)

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