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 $ \rho $ = 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, $ \pi r^{2}h _{1}=\pi {{(nr)}^{2}}h _{2} $
therefore $ h _{1}=n^{2}h _{2} $
Now, pressure at point A = pressure at point B $ h\rho g=(h _{1}+h _{2})\rho ‘g $
therefore h = $ (n^{2}h _{2}+h _{2})sg $
As $ \left( s=\frac{\rho ‘}{\rho } \right) $
therefore $ h _{2}=\frac{h}{(n^{2}+1)s} $
