If one could transport a simple pendulum of constant length from the Earth's surface to the Moon's,where the acceleration due to gravity is one-sixth (1/6)that on the Earth,by what factor would the pendulum frequency be changed?
A)about 6.0
B)about 2.5
C)about 0.41
D)about 0.17

Question

Quizplus · Accepted Answer

The frequency of a simple pendulum is given by the equation f=1/(2π)√(g/L), where g is the acceleration due to gravity and L is the length of the pendulum. Since g on the Moon is one-sixth that on Earth, the frequency would be f=1/(2π)√((1/6)g/L)=1/(2π)√((1/6)(9.81 m/s^2)/L)=1/(2π)√(1.635/L). Since the length of the pendulum is constant, the frequency would decrease by a factor of √(1.635/L) when moving from Earth to the Moon. Therefore, the factor by which the pendulum frequency would be changed is approximately 0.41.

If One Could Transport a Simple Pendulum of Constant Length