A V-shaped glass tube of uniform cross section is kept in a vertical plane as shown. A liquid is poured in the tube. In equilibrium the level of liquid in both limbs of tube are equal. Find the angular frequency of small oscillation of liquid.

Options

A. `(g sin alpha. sin beta)/(sqrt(h))`
B. `sqrt((g sin alpha.sin beta)/(h))`
C. `sqrt((g)/(h))`
D. `sqrt((g(sin alpha+sin beta))/(h))`

Answer

B

Explanation

The diagram in disturbed condition is:

`:. Deltal =x +x' ………(1)` From diagram:

`y = x sin alpha =x' sin beta rArr x' =((sin alpha)/(sin beta)) x: ….(2)`
`:.` Restoring force, `F = W_(Deltal).sin beta`
`= (rho A. Deltal.g) sin beta ..........(3)`
But `F = ma...........(4)`
where `m = A rho.l ............(5)`
`l = (h)/(sin alpha) +(h)/(sin beta) ..........(6)`
find `w`, after aolving above equations.