Physics-
General
Easy

Question

A simple pendulum of length  has a bob of mass  with a charge  on it. A vertical sheet of change, with surface charge density  passes through the point of suspension. At equilibrium, the spring makes an angle theta  with the vertical. Its time period of oscillations is T in this position. Then

  1. tan invisible function application theta equals fraction numerator sigma straight q over denominator 2 epsilon subscript 0 mg end fraction
  2. tan invisible function application theta equals fraction numerator sigma straight q over denominator epsilon subscript 0 mg end fraction
  3. straight T greater than 2 pi square root of 1 over straight g end root
  4. T equals 2 pi square root of 1 over g end root

The correct answer is: tan invisible function application theta equals fraction numerator sigma straight q over denominator 2 epsilon subscript 0 mg end fraction


    Electric intensity at  due to sheet of charge,
    E equals 1 half sigma over epsilon subscript 0
    force on the bob due to sheet of charge
    straight F equals qE equals 1 half fraction numerator sigma straight q over denominator epsilon subscript 0 end fraction
    As the bob is in equilibrium, so

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell mg over OC equals straight F over CB equals straight T over BO end cell row cell tan invisible function application theta equals CB over OC equals straight F over mg end cell row cell equals fraction numerator 1 half sigma straight q divided by epsilon subscript 0 over denominator mg end fraction equals fraction numerator sigma straight q over denominator 2 epsilon subscript 0 mg end fraction end cell end table

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