One end of a V-tube containing mercury is connected to a suction pump and the other end to atmosphere. The two arms of the tube are inclined to horizontal at an angle of 45° each. A small pressure difference is created between two columns when the suction pump is removed. Will the column of mercury in V-tube execute simple harmonic motion? Neglect capillary and viscous forces. Find the time period of oscillation.

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Payal Gupta | Contributor-Level 10

7 months ago

This is a long answer type question as classified in NCERT Exemplar

Let us consider an infinitesimal liquid column of length dx at a height x from horizontal line.

If $ρ =$ density of the liquid

PE= dmgx=A $ρ d x g x$

So total PE of the column

= $\int_{0}^{h_{1}} A d x g ρ x$ = $A g ρ \int_{o}^{h_{1}} x d x = A ρ g \frac{h_{1}^{2}}{2}$

But h₁=lsin45

PE=A $ρ$ gl²sin²45/2

Similarly PE of right column = A $ρ$ gl

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Physics NCERT Exemplar Solutions Class 11th Chapter Fourteen 2025

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