Question

If a pendulum clock keeps perfect time at the base of a mountain, will it also keep perfect time when it is moved to the top of the mountain? Explain.

Short answer

No. It won’t keep perfect time when it is moved to the top of the mountain.

Step-by-step solution

Relationship between displacement and time period

A simple pendulum of length L can be modeled to move in simple harmonic motion for small angular displacements from the vertical. Its period is

$T=2\pi \sqrt{\frac{L}{g}}$

T = Time period of oscillation

L = Length of string

g = Gravitational acceleration

Explain the reasoning

• The period of a pendulum depends on the acceleration of gravity $T=2\pi \sqrt{\frac{L}{g}}$.
• If the acceleration of gravity is different at the top of the mountain, the period is different and the pendulum does not keep perfect time.
• Two things will affect the acceleration of gravity; the top of the mountain is farther from the center of the Earth, and the nearby large mass of the mountain under the pendulum.