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 |
Where M is mass of filled liquid and I is length of tube. |
Force on this element |
\[dF=dm\times x{{\omega }^{2}}\] |
\[\int\limits_{0}^{F}{dF=\frac{M}{L}{{\omega }^{2}}\int\limits_{0}^{L}{x\,dx}}\] |
or \[F=\frac{M}{L}{{\omega }^{2}}\left[ \frac{{{L}^{2}}}{2} \right]=\frac{ML{{\omega }^{2}}}{2}\] |
or \[F=\frac{1}{2}ML{{\omega }^{2}}\] |
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