151k views
3 votes
At what rate will a pendulum clock run on Mars, where the acceleration due to gravity is 3.73 m/s², if it keeps time accurately on Earth? That is, find the time (in hours) it takes the clock\'s minute hand to make one revolution on Mars.

1 Answer

4 votes

Final answer:

A pendulum clock on Mars will run at a rate where the minute hand takes approximately 20.43 minutes to make one revolution.

Step-by-step explanation:

A pendulum clock runs based on the length of its pendulum and the acceleration due to gravity. The formula for the period of a pendulum is T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. To find the rate at which the pendulum clock runs on Mars, where the acceleration due to gravity is 3.73 m/s², we can use the formula and compare it to the rate on Earth.

Let's assume the pendulum clock on Earth takes one hour for the minute hand to make one revolution. In this case, the period would be 60 minutes.

Using the formula, we can rearrange it to solve for L:

L = (T/2π)² * g

Substituting the known values, we get:

L = (60/2π)² * 9.8 ≈ 0.994 meters

Now we can calculate the period on Mars:

T = 2π√(L/g) = 2π√(0.994/3.73) ≈ 20.43 minutes

Therefore, on Mars, it would take approximately 20.43 minutes for the pendulum clock's minute hand to make one revolution.

User Dan Homerick
by
8.9k points