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Physics Assignment Help| Oscillation of Liquid Column in a UTube|www.expertsmind.com Oscillation of f L Liquid Column in a U-Tube
If a liquid is taken in a U-tube, it maintains equal level in both the columns of the tube. When air is blown in on side B, the liquid may go down upto point D. The displacement of the liquid is given by BD = x. In the second column, the liquid goes up to E and the displacement displacement is CE = x. As the applied force is withdrawn, the liquid level level in the second column comes down because because of gravity from E to C. But due to inertia, it overshoots the mark C and goes to F (CF = x), whereas the liquid in the other column also goes up by the same distance. Thus, the liquid starts oscillating in both the columns. This motion of the liquid in the U-tube U -tube is SHM as explained below. Suppose density of the liquid =
Height of the liquid column in each column = h E
Area of cross section of every column = A B
C
2x C
B x
Displacement of the liquid = x
F
D h
Here
a
g h
….. (i)
x
(a)
Since
g h
= constant, therefore a
(b)
x
Hence the motion of the liquid column in the U-tube is S.H.M. The time time period period of oscil oscillati lation on is shown shown by T 2
Using equation (i), we get T 2
displacement acceleration
2
h g
This gives the time period of oscillations of the liquid in the U-tube.