Motion of an oscillating liquid column in a U-tube is

Options

A. periodic but not simple harmonic
B. non-periodic
C. simple harmonic and time period is independent of the density of the liquid
D. simple harmonic and time period is directly proprotional to the density of the liquid

Answer

C

Explanation

Consider the diagram in which a liquid column oscillates. In this caes, restoring force acts on the liquid due to gravity. Acceleration of the liquid column, can be calculated in terms of restoring force.

Restoring force f=Weight of liquid column of height 2y
`rArrf=-(Axx2yxxp)xxg=-2Apgy` `[:.eta=pv]`
`rArrf=prop-yrArr` Motion is SHM with force constant `k=2Apg`.
`rArr` Time period `T=2pisqrt((m)/(k))=2pisqrt(Axx2hxxp)/(2Apg)=2pisqrt((h)/(g)`
`T=2pisqrt(l)/(g),` where l=h
Which is independent of the density of the liquid.