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A cylinder of radius R and height H is f...

A cylinder of radius `R` and height `H` is foam unknown height `h`. When is rotated at an unknown constant angular velocity `omega`, the base of the cylinder gets exposed when the liquid just starts spilling out, as shown in Fig.
a. Find the height `h` of the liquid.
b. Find the angular speed `w` of the cylinder.

Text Solution

Verified by Experts

Since the original level of water before rotation is equal to the average of the minimum and maximm water level after rotation, therefore
`h=(+H)/2`
b. The equation of the parabolic surface is
`y=(omega^(2)r^(2))/(2g)` (`:.y_(0)=0)`
We know that for `r=R, y=H`, thus
`H=(omega^(2)R^(2))/(2g)` or `omega=sqrt((2gH))/R`
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