Physics-
General
Easy

Question

A bob of mass M is suspended by a massless string of length L. The horizontal velocity V at position A is just sufficient to make it reach the point B. The angle theta at which the speed of the bob is half of that at A, satisfies

  1. theta equals fraction numerator pi over denominator 4 end fraction    
  2. fraction numerator pi over denominator 4 end fraction less than theta less than fraction numerator pi over denominator 4 end fraction    
  3. fraction numerator pi over denominator 2 end fraction less than theta less than fraction numerator 3 pi over denominator 4 end fraction    
  4. fraction numerator 3 pi over denominator 4 end fraction less than theta less than pi    

The correct answer is: fraction numerator 3 pi over denominator 4 end fraction less than theta less than pi


    V to the power of 2 end exponent equals U to the power of 2 end exponent minus 2 g left parenthesis L minus L cos invisible function application theta right parenthesis
    fraction numerator 5 g L over denominator 4 end fraction equals 5 g L minus 2 g L left parenthesis 1 minus cos invisible function application theta right parenthesis

    5 equals 20 minus 8 plus 8 cos invisible function application theta
    cos invisible function application theta equals negative fraction numerator 7 over denominator 8 end fraction
    fraction numerator 3 pi over denominator 4 end fraction less than theta less than pi

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