Physics-
General
Easy

Question

A particle of mass m, initially at rest, is acted upon by a variable force F for a brief interval of time T. It begins to move with a velocity u after the force stops acting. F is shown in the graph as a function of time. The curve is a semicircle.

  1. u equals fraction numerator pi F subscript 0 end subscript superscript 2 end superscript over denominator 2 m end fraction    
  2. u equals fraction numerator pi T to the power of 2 end exponent over denominator 8 m end fraction    
  3. u equals fraction numerator pi F subscript 0 end subscript T over denominator 4 m end fraction    
  4. u equals fraction numerator F subscript 0 end subscript T over denominator 2 m end fraction    

The correct answer is: u equals fraction numerator pi F subscript 0 end subscript T over denominator 4 m end fraction


    Initially particle was at rest. By the application of force its momentum increases.
    Final momentum of the particle equalsArea of F - t graph
    Þ m u equalsArea of semi circle
    m u equals fraction numerator pi   r to the power of 2 end exponent over denominator 2 end fraction equals fraction numerator pi   r subscript 1 end subscript r subscript 2 end subscript over denominator 2 end fraction equals fraction numerator pi   left parenthesis F subscript 0 end subscript right parenthesis   left parenthesis T divided by 2 right parenthesis over denominator 2 end fractionÞu equals fraction numerator pi   F subscript 0 end subscript T over denominator 4 m end fraction

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