Apendulum has a period of 1.69 s on earth. what is its period on mars, where the acceleration of gravity is about 0.37 that on earth?

The formula for the period of the pendulum is

where L is the pendulum's length and g the gravitational acceleration.

Labeling with E the Earth and with M Mars, we can write the period of the pendulum on Earth as

and the period of the pendulum on Mars as


if we calculate the ratio, we get

but we know that the gravitational acceleration on Mars is 0.37 times the gravitational acceleration on Earth:

Substituting into the formula, we find

And so, the period of the pendulum on Mars is