Physics-
General
Easy

Question

A balloon rises from rest with a constant acceleration g divided by 8. A stone is released from it when it has risen to height h. The time taken by the stone to reach the ground is

  1. 4 square root of fraction numerator h over denominator g end fraction end root  
  2. 2 square root of fraction numerator h over denominator g end fraction end root  
  3. square root of fraction numerator 2 h over denominator g end fraction end root  
  4. square root of fraction numerator g over denominator h end fraction end root  

The correct answer is: 2 square root of fraction numerator h over denominator g end fraction end root


    The velocity of balloon at height h, v equals square root of 2 open parentheses fraction numerator g over denominator 8 end fraction close parentheses h end root
    When the stone released from this balloon, it will go upward with velocity, equals fraction numerator square root of g h end root over denominator 2 end fraction (Same as that of balloon). In this condition time taken by stone to reach the ground
    t equals fraction numerator v over denominator g end fraction open square brackets 1 plus square root of 1 plus fraction numerator 2 g h over denominator v to the power of 2 end exponent end fraction end root close square brackets equals fraction numerator square root of g h end root divided by 2 over denominator g end fraction open square brackets 1 plus fraction numerator 2 g h over denominator g h divided by 4 end fraction close square brackets
    equals fraction numerator 2 square root of g h end root over denominator g end fraction equals 2 square root of fraction numerator h over denominator g end fraction end root

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