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3-2.Motion in Plane
hard
A tube of length $50\,cm$ is filled completely with an incompressible liquid of mass $250\,g$ and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity $x \sqrt{ F }$ rad $s ^{-1}$. If $F$ be the force exerted by the liquid at the other end then the value of $x$ will be$....$
A$2$
B$3$
C$1$
D$4$
(JEE MAIN-2022)
Solution
$F =\int_{0}( dm ) \omega^{2} x$$=\int_{0}^{ L }\left(\frac{ m }{ L } dx \right) \omega^{2} x$
$=\frac{ m }{ L } \omega^{2} \frac{ L ^{2}}{2}$
$=\frac{ m \omega^{2} L }{2}$
$\omega=\sqrt{\frac{2}{ mL }} \sqrt{ F }$
$=\sqrt{\frac{2}{0.25 \times 0.5}} \sqrt{ F }$
$=\sqrt{16} \sqrt{ F }$
$=4 \sqrt{ F }$
Standard 11
Physics
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