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3-2.Motion in Plane
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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 $. The force exerted by the liquid at the other end is
A$\frac{{ML{\omega ^2}}}{2}$
B$ML{\omega ^2}$
C$\frac{{M{\omega }L^2}}{2}$
D$\frac{{M{L^2}{\omega ^2}}}{2}$
(IIT-1992) (AIPMT-2006)
Solution
(a) $dM = \left( {\frac{M}{L}} \right)dx$force on $‘dM’$ mass is $dF = (dM)\,{\omega ^2}x$
By integration we can get the force exerted by whole liquid
$⇒$ $F = \int_0^L {\frac{M}{L}} {\omega ^2}x\,dx$ $ = \frac{1}{2}M{\omega ^2}L$
Standard 11
Physics
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