A tube of length 50 cm is filled completely with an incompressible liquid of mass 250g closed both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity $z\sqrt[]{F}rad{s}^{-1}.$  If F be the force exertaed by the liquid at the other end then the value of x will be __________.

$\omega =x\sqrt[]{F}rad/5$

As, F = $m{\omega }^2\frac{L}{2}$

$\Rightarrow F=\frac{mL}{2}\left(x^{2}F\right)\Rightarrow x^2=\frac{2}{mL}=\frac{2}{\frac{1}{4}\times \frac{1}{2}}=16$

$\therefore x=4$

 

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