Physics Two Dimensional Motion Question 28
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 $ \omega $ . The force exerted by the liquid at the other end is
[IIT 1992]
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:
$ 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
Therefore $ F=\int _{0}^{L}{\frac{M}{L}}{{\omega }^{2}}x,dx $
$ =\frac{1}{2}M{{\omega }^{2}}L $
BETA
