A pendulum of length L is suspended from the ceiling of an elevator.When the elevator is at rest the period of the pendulum is T.How does the period of the pendulum change when the elevator moves upward with constant acceleration?
A)The period does not change.
B)The period increases.
C)The period decreases.
D)The period becomes zero.
E)The period increases if the upward acceleration is more than g/2 but decreases if the upward acceleration is less than g/2.

Question

Quizplus · Accepted Answer

The 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. When the elevator moves upward with constant acceleration a, the effective acceleration acting on the pendulum is g + a.

Using this effective acceleration in the formula for the period of the pendulum, we get:

T' = 2π √(L/(g+a))

Since g + a is larger than g, the square root term in the above formula is smaller than the square root term in the original formula for T. Therefore, T' is smaller than T, which means the period of the pendulum decreases when the elevator moves upward with constant acceleration.

Therefore, the correct choice is C.

A Pendulum of Length L Is Suspended from the Ceiling