Physics-
General
Easy

Question

There is a simple pendulum hanging from the ceiling of a lift. When the lift is stand still, the time period of the pendulum is T . If the resultant acceleration becomes straight g divided by 4 , then the new time period of the pendulum is

  1. 0.8 straight T
  2. 0.25 straight T
  3. 2 T
  4. 4 T

The correct answer is: 2 T


    Time period of a simple pendulum of length , is given by
    straight T equals 2 pi square root of straight l over straight g end root times left parenthesis straight i right parenthesis
    Where, g is acceleration due to gravity.
    When g to the power of straight prime equals g over 4 comma
    New, time period is
    straight T to the power of straight prime equals 2 pi square root of fraction numerator straight l over denominator straight g divided by 4 end fraction end root times left parenthesis ii right parenthesis
    Dividing Eq. (ii) by Eq. (i), we get
    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 straight T to the power of straight prime over straight T equals square root of fraction numerator straight g over denominator straight g divided by 4 end fraction end root equals 2 end cell row cell not stretchy rightwards double arrow straight T to the power of straight prime equals 2 straight T end cell end table
    Hence, new time period becomes twice of the original value

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