a liquid of density p is filled in a U tube of uniform cross section up to a Hight h. if the liquid in one limit of the tube is pressed slightly downward and then left , the liquid column executes vertical oscillation assuming that the period of oscillation may depend on h, p and g . find a possible formula for t by the method of dimensions.
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Answer:
Equation of motion for the liquid can be given by
m
dt
2
d
2
x
=−2xadg, where a is the cross section of the u tube.
⇒
dt
2
d
2
x
+
m
2adg
x=0
⇒
dt
2
d
2
x
+ω
0
2
x=0,
where ω
0
2
=
m
2adg
⇒
T
2π
=
m
2adg
⇒T=2π
2adg
m
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