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22 December, 11:33

If the period of a simple pendulum is T and you increase its length so that it is 4 times longer, what will the new period be? a. T/4b. It is unchanged. C. T/2 d. 2T e. 4T

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  1. 22 December, 13:09
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    d. 2T

    Explanation:

    Period of a simple pendulum: This can be defined as the time taken for a simple pendulum to complete an oscillation.

    The S. I unit of the period of a simple pendulum is second (s).

    Mathematically the period of a simple pendulum can be represented as

    T = 2π√ (L/g) ... Equation 1

    Where T = period of the pendulum, L = length of the pendulum, g = acceleration due to gravity, π = pie.

    Note: If the length of a simple pendulum is increased, the period will also increase, while acceleration due to gravity is constant.

    Hence,

    T' = 2π√ (4L/g) ... Equation 2

    Where T' is the new period when the length of the pendulum is increased by 4 time its original length.

    Dividing equation 1 by equation 2

    T/T' = 2π√ (L/g) / 2π√ (4L/g)

    T/T' = √L/2√L

    T/T' = 1/2

    T' = 2T

    Thus, the right option is d. 2T
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