Physics-
General
Easy

Question

Water is filled in a cylindrical container to a height of 3m. The ratio of the cross-sectional area of the orifice and the beaker is 0.1. The square of the speed of the liquid coming out from the orifice is (g = 10 m/s2)

  1. 50 m2/s2    
  2. 50.5 m2/s2    
  3. 51 m2/s2    
  4. 52 m2/s2    

The correct answer is: 50 m2/s2


    Let A = cross-section of tank
    a = cross-section hole
    V = velocity with which level decreases
    v = velocity of efflux

    From equation of continuity a v equals A V rightwards double arrow V equals fraction numerator a v over denominator A end fraction
    By using Bernoulli's theorem for energy per unit volume
    Energy per unit volume at point A
    = Energy per unit volume at point B
    P plus rho g h plus fraction numerator 1 over denominator 2 end fraction rho V to the power of 2 end exponent equals P plus 0 plus fraction numerator 1 over denominator 2 end fraction rho v to the power of 2 end exponent
    Þ v to the power of 2 end exponent equals fraction numerator 2 g h over denominator 1 minus open parentheses fraction numerator a over denominator A end fraction close parentheses to the power of 2 end exponent end fraction equals fraction numerator 2 cross times 10 cross times left parenthesis 3 minus 0.525 right parenthesis over denominator 1 minus left parenthesis 0.1 right parenthesis to the power of 2 end exponent end fraction equals 50 left parenthesis m divided by sec invisible function application right parenthesis to the power of 2 end exponent

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