14.19 One end of a U-tube containing mercury is connected to a suction pump and the other end to atmosphere. A small pressure difference is maintained between the two columns. Show that, when the suction pump is removed, the column of mercury in the U-tube executes simple harmonic motion.

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Vishal Baghel | Contributor-Level 10

8 months ago

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 = - (Volume $* d e n s i t y * g)$

F = -(A $* 2 h * ρ * g)$ = -2A $ρ g$ = -k $* d i s p l a c e m e n t i n o n e o f t h e a r m s (h)$

Where, 2h is the height of the mercury columns in two arms

The constant k is given by k = $- \frac{F}{h}$ = 2A

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physics ncert solutions class 11th 2023

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