Figure shows a three arm tube in which a liquid is filled upto levels of height $l$. It is now rotated at an angular frequency $\omega$ about an axis passing through arm $B$. The angular frequency $\omega$ at which level of liquid in arm $B$ becomes zero.
A$\sqrt {\frac{{2g}}{{3{\rm{l}}}}} $
B$\sqrt {\frac{g}{{\rm{l}}}} $
C$\sqrt {\frac{{3g}}{{\rm{l}}}} $
D$\sqrt {\frac{{3g}}{{2{\rm{l}}}}} $
Diffcult
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C$\sqrt {\frac{{3g}}{{\rm{l}}}} $
c $P=P_{0}+\rho g\left(\frac{3 l}{2}\right)=P_{0}+\frac{3 \rho g l}{2}$
$\frac{3 \rho g l S}{2}=\frac{\rho S l^{2}}{2} \omega^{2}$
$\frac{3}{2} g=\frac{l \omega^{2}}{2}$
$\omega^{2}=\frac{3 g}{l}$
$\omega=\sqrt{\frac{3 g}{l}}$
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