A) \[\frac{ML{{\omega }^{2}}}{2}\]
B) \[\frac{M{{L}^{2}}\omega }{2}\]
C) \[ML{{\omega }^{2}}\]
D) \[\frac{M{{L}^{2}}{{\omega }^{2}}}{2}\]
Correct Answer: D
Solution :
Let the length of a small element of tube be \[dx.\]Mass of this element \[dm=\frac{M}{L}dx\] Where M is mass of filled liquid and L is the length of tube. Face on this element \[dF=(dm){{\omega }^{2}}x=\left( \frac{M}{L} \right)dx.{{\omega }^{2}}x\] Integrating \[\int_{0}^{F}{dF}=\frac{M}{L}{{\omega }^{2}}\int_{0}^{L}{x\,dx}\] or \[F=\frac{M}{L}{{\omega }^{2}}\left[ \frac{{{L}^{2}}}{2} \right]=\frac{ML{{\omega }^{2}}}{2}\] or \[F=\frac{1}{2}ML{{\omega }^{2}}\]You need to login to perform this action.
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