SHMMedium
Question
A vertical U-tube contains a liquid. The total length of the liquid column inside the tube is l. When the liquid is in equilibrium, the liquid surface in one of the arms of the U-tube is pushed down slightly and released. The entire liquid column will undergo a periodic motion : -
Options
A.The motion is not simple harmonic motion.
B.The motion is simple harmonic motion.
C.If it undergoes simple harmonic motion, the time period will be 
D.It is undergoes simple harmonic motion,the time period will be 
Solution
If one surface is pushed down by x the other surface moves up by x.
Net unbalanced force on the liquid column
= 2xAρg
mass of the liquid column = lAρ
⇒ - 2xAρg = (lAρ) a ⇒ a =
∵ a = - ω2x ⇒ ω =
Net unbalanced force on the liquid column
= 2xAρg
mass of the liquid column = lAρ
⇒ - 2xAρg = (lAρ) a ⇒ a =
∵ a = - ω2x ⇒ ω =
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