Physics-
General
Easy

Question

A small sphere carrying a charge q is hanging in between two parallel plates
by a string of length L. Time period of pendulum is T subscript 0 end subscript. When parallel plates are
charged, the time period changes to T. The ratio T divided by T subscript 0 end subscriptis equal to

  1. open parentheses fraction numerator g plus fraction numerator q E over denominator m end fraction over denominator g end fraction close parentheses to the power of 1 divided by 2 end exponent    
  2. open parentheses fraction numerator g over denominator g plus fraction numerator q E over denominator m end fraction end fraction close parentheses to the power of 3 divided by 2 end exponent    
  3. open parentheses fraction numerator g over denominator g plus fraction numerator q E over denominator m end fraction end fraction close parentheses to the power of 1 divided by 2 end exponent    
  4. None of these    

The correct answer is: open parentheses fraction numerator g over denominator g plus fraction numerator q E over denominator m end fraction end fraction close parentheses to the power of 1 divided by 2 end exponent


    The motion of sphere is simple harmonic. It’s time period (T subscript 0 end subscript) is given by

    T subscript 0 end subscript equals 2 pi square root of fraction numerator l over denominator g end fraction end root (i)
    where l is length of string, g the acceleration due to gravity.
    When sphere is placed in electric field. (E) force due to electric field acts on the sphere-1
    F subscript E end subscript equals q E equals m g
    where q is charge on sphere.
    Hence, resultant acceleration is
    g to the power of ´ end exponent equals g plus fraction numerator q E over denominator m end fraction
    therefore T equals 2 pi square root of fraction numerator l over denominator g plus fraction numerator q E over denominator m end fraction end fraction end root (ii)
    Dividing Eq. (ii) by Eq. (i), we get
    fraction numerator T over denominator T subscript 0 end subscript end fraction equals square root of fraction numerator g over denominator g plus fraction numerator q E over denominator m end fraction end fraction end root

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