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 ω. The force exerted by the liquid at the other ends is :

Question

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 ω. The force exerted by the liquid at the other ends is :

Infinity Learn · Accepted Answer

Consider a small mass element dm at a distance x from axis of rotation.Required force $$F=$$∫$$dF=$$∫(dm)ω$$2x=$$∫$$0L$$ MLω$$2xdx=M$$ω$$2L2OR$$ As force on element dF∝x so total force $$=$$ Average forceTherefore $$F=0+M$$ω$$2L2=M$$ω$$2L2$$

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 $ω$ . The force exerted by the liquid at the other ends is :

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