wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

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

A
periodic but not simple harmonic
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
non- periodic
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
simple harmonic and time is independent of the density of the liquid
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
simple harmonic and time period is directly proportional to the density of the liquid
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C simple harmonic and time is independent of the density of the liquid
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.

Let h be height of liquid in each limb of U tube,
y be drop in height of of liquid column in one of the limbs
Restoring force f= Weight of the column of height 2y
f=(A×2y×ρ)×g=2Aρgy [m=ρv]
ma=2Aρgy [m=ρv]
ay
Motion is SHM with force consant k=2Aρg.
Time period T=2πmk=2πA×2h×ρ2Aρg=2πhg
T=2πlg, where l=h
Which is independent of the density of the liquid.

flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon