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Asked by Anil Last Modified
Answer 
Harshit Bhardwaj
Area of cross-section of the U-tube = A
Density of the mercury column = ρ
Acceleration due to gravity = g
Restoring force, F = Weight of the mercury column of a certain height
F = –(Volume × Density × g)
F = –(A × 2h × ρ ×g) = –2Aρgh = –k × Displacement in one of the arms (h)
Where,
2h is the height of the mercury column in the two arms
k is a constant, given by 
Time period, 
Where,
m is the mass of the mercury column
Let l be the length of the total mercury in the U-tube.
Mass of mercury, m = Volume of mercury × Density of mercury
= Alρ
∴
Hence, the mercury column executes simple harmonic motion with time period
.
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