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QJEEM20Ph4a05: JEE Main 2020 Physics - Class 11 JEEM20Ph4a05 Solution: A cylindrical vessel containing a liquid is rotated about its…

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\omega rad s–1. The difference in the height, h (in cm) of liquid at the centre of vessel and at the side will be : JEE Main 2020 (Online) 2nd September Morning Slot Physics - Properties of Matter Question 196 English

Multiple Choice Options

  • A 2ω225g{{2{\omega ^2}} \over {25g}}
  • B 5ω22g{{5{\omega ^2}} \over {2g}}
  • C 25ω22g{{25{\omega ^2}} \over {2g}}
  • D 2ω25g{{2{\omega ^2}} \over {5g}}

Step-by-Step Verified Solution

JEE Main 2020 (Online) 2nd September Morning Slot Physics - Properties of Matter Question 196 English Explanation

Applying pressure equation from A to B

P0 + ρ\rho . Rω22{{R{\omega ^2}} \over 2} .R - ρ\rho gh = P0

⇒\Rightarrow ρR2ω22{{\rho {R^2}{\omega ^2}} \over 2} = ρ\rho gh

⇒\Rightarrow h = R2ω22{{{R^2}{\omega ^2}} \over 2} = (5)2ω22g{\left( 5 \right)^2}{{{\omega ^2}} \over {2g}} = 252ω2g{{25} \over 2}{{{\omega ^2}} \over g}

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