A giant simple pendulum has a time period of 5.0 s. If , what would be the change in pendulum's length if the period decreases to 4.5 s?
A) 1.2 m shorter
B) 0.8 m longer
C) 1.2 m longer
D) 0.8 m shorter
E) The length would not change.

Question

A giant simple pendulum has a time period of 5.0 s. If , what would be the change in pendulum's length if the period decreases to 4.5 s?
A) 1.2 m shorter
B) 0.8 m longer 
C) 1.2 m longer
D) 0.8 m shorter
E) The length would not change.

Quizplus · Accepted Answer

The time period of a simple pendulum is given by:T = 2π√(L/g)where L is the length of the pendulum and g is the acceleration due to gravity.If the time period decreases, then the length of the pendulum must decrease.The change in length is given by:ΔL = L - L' = L(1 - (T'/T)^2)where L' is the new length of the pendulum and T' is the new time period.Substituting the given values, we get:ΔL = L(1 - (4.5 s/5.0 s)^2) = 0.12 LTherefore, the length of the pendulum would be 1.2 m shorter.

A Giant Simple Pendulum Has a Time Period of 5