Answered

Select the correct answer.

The gravity on Mars is [tex]3.69 \, \text{m/s}^2[/tex]. If you had a pendulum on Mars that was 1.8 meters long, what would the period be?

A. 3.9 seconds
B. 3.2 seconds
C. 0.87 seconds
D. 5.2 seconds
E. 4.4 seconds



Answer :

To determine the period of a pendulum on Mars, we use the formula for the period [tex]\( T \)[/tex], which is given by:

[tex]\[ T = 2\pi \sqrt{\frac{L}{g}} \][/tex]

Where:
- [tex]\( T \)[/tex] is the period of the pendulum,
- [tex]\( \pi \)[/tex] (pi) is approximately 3.14159,
- [tex]\( L \)[/tex] is the length of the pendulum (1.8 meters in this case),
- [tex]\( g \)[/tex] is the acceleration due to gravity (3.69 meters/second[tex]\(^2\)[/tex] on Mars).

Substitute [tex]\( L \)[/tex] and [tex]\( g \)[/tex] into the formula:

[tex]\[ T = 2\pi \sqrt{\frac{1.8}{3.69}} \][/tex]

Next, perform the calculations in steps:

1. Calculate the division inside the square root:

[tex]\[ \frac{1.8}{3.69} \][/tex]

2. Take the square root of the result from step 1:

[tex]\[ \sqrt{\frac{1.8}{3.69}} \][/tex]

3. Multiply the result by [tex]\( 2\pi \)[/tex]:

[tex]\[ 2\pi \sqrt{\frac{1.8}{3.69}} \][/tex]

The solution to these calculations gives us the period of the pendulum. The correct period is approximately 4.4 seconds.

Thus, the correct answer is:

O E. 4.4 seconds