Kinematics Question 483

Question: A tube of length $ L $ it’s filled completely with an incompressible liquid of mass $ M $ and closed at both the ends. The tube it’s then rotated in a horizontal plane about one of it’s ends with a uniform angular velocity $ \omega $ . The force exerted by the liquid at the other end it’s [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} $

Show Answer

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}}xdx $

$ =\frac{1}{2}M{{\omega }^{2}}L $



NCERT Chapter Video Solution

Dual Pane