A closed of length `l` containing a liquid of variable density `rho(x)=rho_(0)(1+alphax)` find the net force exerted by the liquid on the axis of rotation. (take the cylinder to be massless and `A=` cross sectional area of cylinder)
(a). `rho_(0)Aomega^(2)l^(2)[(1)/(2)+(1)/(3)alphal]`
(b). `rho_(0)Aomega^(2)l^(2)[(1)/(2)+(2)/(3)alphal]`
(c). `rho_(0)Aomega^(2)l^(2)[(1)/(2)+alphal]`
(d). `rho_(0)Aomega^(2)l^(2)[(1)/(2)+(4)/(3)alphal]`

Answer

A

Explanation

`dm=rhoAdx,dF=(dm)omega^(2)x impliesF=underset(0)overset(l)intomega^(2)xrhoAdx=omega^(2)rho_(0)Aunderset(0)overset(l)(1+alphax)xdx=rho_(0)Aomega^(2)l^(2)((1)/(2)+(1)/(3)alphal)`