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} $
Show Answer
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} $
