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: A
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 length of tube. Force on this element, \[d\,F=dm\times x{{\omega }^{2}}\] \[\int_{0}^{F}{dF\,=\frac{M}{L}{{\omega }^{2}}\int_{0}^{L}{x\,\,dx}}\] 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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