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A cylinder of radius R = 1 m and height ...

A cylinder of radius `R = 1 m` and height `H = 3 m` two- thirds filled with water, is rotated about its vertical axis as shown in Fig. Determine the speed of rotation when
a. the: water just starts spilling over the rim.
b. the point at the centre of the base is just exposed.

Text Solution

Verified by Experts

We know that `y_("max")=H=3m`
`h=2/3H=2m`
`R=1m,g=10m//s^(2)`

Thus `omega=sqrt((4g(H-h))/R^(2))=sqrt((4(10)(3-2))/1^(2))=sqrt(40)rad//s`
b. We know that
`y=(omegar^(2))/(2g)=y_(0)`
Here `y=H=3m,y_(0)=0, r=R=1m, g=0m//s^(2)`
`omega=sqrt((2gH)/(R^(2)))=sqrt((2(10)(3))/1^(2))=sqrt60rad//s`
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