1.

A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity omega. The force exerted by the liquid at the other end is

Answer»

`(Momega^(2)L)/2`
`Momega^(2)L`
`(Momega^(2)L)/4`
`(Momega^(2)L^(2))/2`

Solution :MASS of liquid in unit length =`M/L`
`therefore` Mass in eIement dx=`(Mdx)/L`
`therefore` Centripetal force =`((Mdx)/L)xomega^(2)`
or `dF=(Momega^(2))/Lxdx`
`thereforeintdF=int_(0)^(L)(Momega^(2))/Lxdx`
or `F=(Momega^(2))/L[(x^(2))/2]_(0)^(L)=(ML^(2)omega^(2))/(2L)` or `F=(MLomega^(2))/2`


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