A V-shaped glass tube of uniform cross-section is kept in a vertical plane as shown. The angular frequency of small oscillations of liquid in a tube is

The diagram in disturbed condition is:

$\therefore$Restoring force, $F=W_{\mathrm{\Delta }l}\cdot \sin \beta$

$=(\rho A\cdot \mathrm{\Delta }l\cdot g)\sin \beta$ . . . .(3)

But F = ma ......................(4)

where m = A $\mathrm{\rho }$.l ...................(5)

$l=\frac{h}{\sin \alpha }+\frac{h}{\sin \beta }$   . . . . . .(6)

find $\omega$, after solving above equations.