Physics-
General
Easy

Question

A body is thrown vertically upwards. If air resistance is to be taken into account, then the time during which the body rises is

  1. Equal to the time of fall  
  2. Less than the time of fall  
  3. Greater than the time of fall  
  4. Twice the time of fall  

The correct answer is: Less than the time of fall


    Let the initial velocity of ball be u
    Time of rise t subscript 1 end subscript equals fraction numerator u over denominator g plus a end fraction and height reached equals fraction numerator u to the power of 2 end exponent over denominator 2 open parentheses g plus a close parentheses subscript blank end fraction
    Time of fall t subscript 2 end subscript is given by
    fraction numerator 1 over denominator 2 end fraction open parentheses g minus a close parentheses t subscript 2 end subscript superscript 2 end superscript equals fraction numerator u to the power of 2 end exponent over denominator 2 open parentheses g plus a close parentheses end fraction
    rightwards double arrow t subscript 2 end subscript equals fraction numerator u over denominator square root of open parentheses g plus a close parentheses open parentheses g minus a close parentheses end root end fraction equals fraction numerator u over denominator open parentheses g plus a close parentheses end fraction square root of fraction numerator g plus a over denominator g minus a end fraction end root
    therefore t subscript 2 end subscript greater than t subscript 1 end subscript because fraction numerator 1 over denominator g plus a end fraction less than fraction numerator 1 over denominator g minus a end fraction

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