A particular pendulum on Earth has a period of 1.00 s. When transported to the moon, where the gravitational acceleration is 1/6 that on Earth, the period of the pendulum would be
A) 0.41
B) 1.00 s
C) 2.4 s
D) 4.1 s
E) 6.0 s

Question

Quizplus · Accepted Answer

The period, T of a simple pendulum is given by the formula:

T = 2π√(L/g)

where L is the length of the pendulum and g is the acceleration due to gravity.

Since the gravitational acceleration on the moon is 1/6 that on Earth, g on the moon would be (1/6)gE, where gE is the acceleration due to gravity on Earth.

Therefore, the period of the pendulum on the moon would be:

T' = 2π√(L/(1/6 gE))

= 2π√(6L/gE)

= 2π(√6/√gE) √L

Since the length of the pendulum does not change, the new period of the pendulum on the moon would be proportional to √(1/gE).

Using gE = 9.81 m/s^2, we have:

T'/T = √(1/(1/6)) = √6

T' = (2.4 s) * (2.45) ≈ 5.88 s

Therefore, the best choice is C) 2.4 s.

A Particular Pendulum on Earth Has a Period of 1