Laws Of Motion Question 139

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 horizontal plane about one of its ends with a uniform angular velocity $ \omega $ . The force exerted by the liquid at the other end is

Options:

A) $ \frac{ML{{\omega }^{2}}}{2} $

B) $ ML{{\omega }^{2}} $

C) $ \frac{ML{{\omega }^{2}}}{4} $

D) $ \frac{ML^{2}{{\omega }^{2}}}{2} $

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Answer:

Correct Answer: A

Solution:

[a] $ dM=( \frac{M}{L} )dx $

Force on dM mass is $ dF=(dM){{\omega }^{2}}x $

By integration, we can get the force exerted by whole liquid

$ \Rightarrow F=\int _{0}^{L}{\frac{M}{L}{{\omega }^{2}}xdx=\frac{1}{2}M{{\omega }^{2}}L} $



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