Physics-
General
Easy

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

  1. fraction numerator n to the power of 2 end exponent h over denominator left parenthesis n plus 1 right parenthesis to the power of 2 end exponent s end fraction    
  2. fraction numerator h over denominator left parenthesis n to the power of 2 end exponent plus 1 right parenthesis s end fraction    
  3. fraction numerator h over denominator left parenthesis n plus 1 right parenthesis to the power of 2 end exponent s end fraction    
  4. fraction numerator h over denominator n to the power of 2 end exponent s end fraction    

The correct answer is: fraction numerator h over denominator left parenthesis n to the power of 2 end exponent plus 1 right parenthesis s end fraction



    If the level in narrow tube goes down by h1 then in wider tube goes up to h2,
    Now, pi r to the power of 2 end exponent h subscript 1 end subscript equals pi left parenthesis n r right parenthesis to the power of 2 end exponent h subscript 2 end subscriptÞ h subscript 1 end subscript equals n to the power of 2 end exponent h subscript 2 end subscript
    Now, pressure at point A = pressure at point B
    h rho g equals left parenthesis h subscript 1 end subscript plus h subscript 2 end subscript right parenthesis rho ´ g
    Þ h = left parenthesis n to the power of 2 end exponent h subscript 2 end subscript plus h subscript 2 end subscript right parenthesis s g open parentheses text As end text   s equals fraction numerator rho ´ over denominator rho end fraction close parentheses Þ h subscript 2 end subscript equals fraction numerator h over denominator left parenthesis n to the power of 2 end exponent plus 1 right parenthesis s end fraction

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