Physics-
General
Easy

Question

There are two identical small holes of area of cross-section a on the opposite sides of a tank containing a liquid of density rho. The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which will has to be applied on the tank to keep it in equilibrium is

  1. g h rho a    
  2. fraction numerator 2 g h over denominator rho a end fraction    
  3. 2 rho a g h    
  4. fraction numerator rho g h over denominator a end fraction    

The correct answer is: 2 rho a g h



    Net force (reaction) = F equals F subscript B end subscript minus F subscript A end subscript equals fraction numerator d p subscript B end subscript over denominator d t end fraction minus fraction numerator d p subscript A end subscript over denominator d t end fraction
    equals a v subscript B end subscript rho cross times v subscript B end subscript minus a v subscript A end subscript rho cross times v subscript A end subscript
    \ F equals a rho open parentheses v subscript B end subscript superscript 2 end superscript minus v subscript A end subscript superscript 2 end superscript close parentheses…(i)
    According to Bernoulli's theorem
    p subscript A end subscript plus fraction numerator 1 over denominator 2 end fraction rho v subscript A end subscript superscript 2 end superscript plus rho g h equals p subscript B end subscript plus fraction numerator 1 over denominator 2 end fraction rho v subscript B end subscript superscript 2 end superscript plus 0
    Þ fraction numerator 1 over denominator 2 end fraction rho open parentheses v subscript B end subscript superscript 2 end superscript minus v subscript A end subscript superscript 2 end superscript close parentheses equals rho g h Þ v subscript B end subscript superscript 2 end superscript minus v subscript A end subscript superscript 2 end superscript equals 2 g h
    From equation (i), F equals 2 a rho g h.

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