Question

A closed cylinder of length 'l ' containing a liquid of variable density r(x) = r₀ (1 + ax) is rotating about a vertical axis with an angular speed w. 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, ignore the gravity) –

• A. r₀ Aw²l²$\left\lbrack \frac{1}{2} + \frac{1}{3}\alpha\mathcal{l} \right\rbrack$
• B. r₀ Aw²l²$\left\lbrack \frac{1}{2} + \frac{2}{3}\alpha\mathcal{l} \right\rbrack$
• C. r₀ Aw²l²$\left\lbrack \frac{1}{2} + \alpha\mathcal{l} \right\rbrack$
• D. r₀ Aw²l²$\left\lbrack \frac{1}{2} + \frac{4}{3}\alpha\mathcal{l} \right\rbrack$

Answer 1

Answer: (A)

r₀ Aw²l²$\left\lbrack \frac{1}{2} + \frac{1}{3}\alpha\mathcal{l} \right\rbrack$

Answer 2

Find center of mass of liquid and then apply centripetal force concept.