Physics-
General
Easy

Question

A cylinder containing water up to a height of 25 cm has a hole of cross-section fraction numerator 1 over denominator 4 end fraction c m to the power of 2 end exponent in its bottom. It is counterpoised in a balance. What is the initial change in the balancing weight when water begins to flow out

  1. Increase of 12.5 gm-wt    
  2. Increase of 6.25 gm-wt    
  3. Decrease of 12.5 gm-wt    
  4. Decrease of 6.25 gm-wt    

The correct answer is: Decrease of 12.5 gm-wt


    Let A = The area of cross section of the hole
    v = Initial velocity of efflux
    d = Density of water,
    Initial volume of water flowing out per second = Av
    Initial mass of water flowing out per second = Avd
    Rate of change of momentum = Adv2
    Initial downward force on the flowing out water = Adv2
    So equal amount of reaction acts upwards on the cylinder.
    \ Initial upward reaction =A d v to the power of 2 end exponent [As v equals square root of 2 g h end root]
    therefore Initial decrease in weight equals A d left parenthesis 2 g h right parenthesis
    equals 2 A d g h equals 2 cross times open parentheses fraction numerator 1 over denominator 4 end fraction close parentheses cross times 1 cross times 980 cross times 25 equals 12.5 gm-wt.

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