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

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