Astronauts on the first trip to mars take along a pendulumthat has a period on earth of 1.50 {\rm s}. the period on mars turns out to be 2.45{\rm s}.what is the free-fall acceleration onmars? gmars= m/s2

3.7 m/s^2

Explanation:

The period of a pendulum is given by:

where L is the length of the pendulum and g is the free-fall acceleration on the planet.

In this problem, we know that the period of the pendulum on Earth is:

while the period of the same pendulum on Mars is

And since the length of the pendulum L does not change, we can write:

where

is the free-fall acceleration on Earth

is the free-fall acceleration on Mars

Re-arranging the equation and substituting numbers, we find: