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Motion of an oscillating liquid column i...

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

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 proportional to the density of the liquid.

Text Solution

Verified by Experts

The correct Answer is:
C
(c) Consider the diagram in which a liquid column oscillates. In this case, 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
`implies f=-(Axx2yxxp)xxg=-2Arhogy" "[because m=rhov]`
`impliesf prop -yimplies` Motion is SHM with force constant `k=2Arhog`.
`implies` Time period `T=2pisqrt((m)/(k))=2pisqrt((Axx2hxxrho)/(2Arhog))=2pisqrt((h)/(g))`
`T=2pisqrt((l)/(g)),` where l=h
Which is independent of the density of the liquid.
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