NCERT Class 11 Physics Solutions: Chapter 14 – Oscillations-Part 13

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Question 14.19:

One end of 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.

Answer:

Area of cross-section of the U-tube

Density of the mercury column

Acceleration due to gravity

Restoring force, Weight of the mercury column of a certain height

Where,

is the height of the mercury column in the two arms

is a constant, given by

Time period,

Where,

is the mass of the mercury column

Let be the length of the total mercury in the U-tube.

Mass of mercury

Hence, the mercury column executes simple harmonic motion with time period is

.