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

1.	Motion of an oscillating liquid column in a U-tube is……..
Answer» periodic but not simple harmonic non-periodic simple harmonic and time period is independent of the density of the liquid simple harmonic and time period is directly PROPORTIONAL to the density of the liquid Solution :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.

Discussion