Physics-
General
Easy

Question

A charged particle q is shot towards another charged particle Q which is fixed, with a speed v. It approaches Q upto a closest distance rand then returns. If q was given a speed 2 v, the closest distance of approach would be

  1. r    
  2. 2 r    
  3. r divided by 2    
  4. r divided by 4    

The correct answer is: r divided by 4


    Let a particle of change qhaving velocity v approaches Q upto a closest distance r and if the velocity becomes 2 v, the closest distance will be r.
    The law of conservation of energy yields,
    Kinetic energy of particle=electric potential energy between them at closest distance of approach.
    Or fraction numerator 1 over denominator 2 end fraction m v to the power of 2 end exponent equals fraction numerator 1 over denominator 4 pi epsilon subscript 0 end subscript end fraction fraction numerator Q subscript q end subscript over denominator r end fraction
    Or fraction numerator 1 over denominator 2 end fraction m v to the power of 2 end exponent equals k fraction numerator Q q over denominator r end fraction (i)
    open parentheses k equals c o n s t a n t equals blank fraction numerator 1 over denominator 4 pi epsilon subscript 0 end subscript end fraction close parentheses
    and fraction numerator 1 over denominator 2 end fraction m open parentheses 2 v close parentheses to the power of 2 end exponent blank equals blank k fraction numerator Q q over denominator r ´ end fraction (ii)
    Dividing Eq. (i) by Eq.(ii),
    fraction numerator fraction numerator 1 over denominator 2 end fraction m v to the power of 2 end exponent over denominator fraction numerator 1 over denominator 2 end fraction m left parenthesis 2 v right parenthesis to the power of 2 end exponent end fraction =fraction numerator fraction numerator k Q q over denominator r end fraction over denominator fraction numerator k Q q over denominator r to the power of ´ end exponent end fraction end fraction
    rightwards double arrow blank fraction numerator 1 over denominator 4 end fraction equals fraction numerator r to the power of ´ end exponent over denominator r end fraction
    rightwards double arrow blank r ’ blank equals fraction numerator r over denominator 4 end fraction

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