SATHEE: Properties Of Solids And Liquids Question 200

Properties Of Solids And Liquids Question 200

Question: Two communicating vessels contain mercury. The diameter of one vessel is n times larger than the diameter of the other. A column of water of height h is poured into the left vessel. The mercury level will rise in the right-hand vessel (s = relative density of mercury and $ρ$ = density of water) by

Options:

A) $\frac{n^{2} h}{{(n + 1)}^{2} s}$

B) $\frac{h}{(n^{2} + 1) s}$

C) $\frac{h}{{(n + 1)}^{2} s}$

D) $\frac{h}{n^{2} s}$

Show Answer

Answer:

Correct Answer: B

Solution:

If the level in narrow tube goes down by h1 then in wider tube goes up to h2,

Now, $π r^{2} h_{1} = π {(n r)}^{2} h_{2}$

therefore $h_{1} = n^{2} h_{2}$

Now, pressure at point A = pressure at point B $h ρ g = (h_{1} + h_{2}) ρ ‘ g$

therefore h = $(n^{2} h_{2} + h_{2}) s g$

As $(s = \frac{ρ ‘}{ρ})$

therefore $h_{2} = \frac{h}{(n^{2} + 1) s}$

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Properties Of Solids And Liquids Question 200

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