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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
With the height difference between the two arms of U-tube are given by 2y.
If the density of liquid is p and coss-section of arms is A. Here the restoring force is provided by the hydrostatic pressure difference
`F= -mg`
`= -Vpg = -(Axx 2y)pg`
`therefore F= -(2A p g)y`
`therefore F propto -y`
The motion of liquid column is SHM. and force constant `k= 2A pg` and periodic time
`T= 2pi sqrt((m)/(k))`
`=2pi sqrt((Axx 2y xx p)/(2A pg))`
`therefore T= 2pi sqrt((y)/(g))`
Putting `y= l`
`therefore T= 2pi sqrt((l)/(g))`
Time period is independent of the density of the liquid.
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