Physics-
General
Easy

Question

A tank is filled with water up to a height H. Water is allowed to come out of a hole P in one of the walls at a depth D below the surface of water. Express the horizontal distance x in terms of H and D

  1. x equals square root of D left parenthesis H minus D right parenthesis end root    
  2. x equals square root of fraction numerator D left parenthesis H minus D right parenthesis over denominator 2 end fraction end root    
  3. x equals 2 square root of D left parenthesis H minus D right parenthesis end root    
  4. x equals 4 square root of D left parenthesis H minus D right parenthesis end root    

The correct answer is: x equals 2 square root of D left parenthesis H minus D right parenthesis end root


    Time taken by water to reach the bottom
    = t equals square root of fraction numerator 2 left parenthesis H minus D right parenthesis over denominator g end fraction end root and velocity of water coming out of hole, v equals square root of 2 g D end root
    \ Horizontal distance covered x equals v cross times t
    = square root of 2 g D end root cross times square root of fraction numerator 2 left parenthesis H minus D right parenthesis over denominator g end fraction end root= 2 square root of D left parenthesis H minus D right parenthesis end root

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