To calculate the period of a pendulum, we use the formula for the period [tex]\( T \)[/tex]:
[tex]\[ T = 2 \pi \sqrt{\frac{L}{g}} \][/tex]
where:
- [tex]\( T \)[/tex] is the period of the pendulum,
- [tex]\( L \)[/tex] is the length of the pendulum,
- [tex]\( g \)[/tex] is the acceleration due to gravity,
- [tex]\( \pi \)[/tex] is a constant approximately equal to 3.14159.
Given the values:
- The gravity on Mars, [tex]\( g_{\text{Mars}} = 3.69 \)[/tex] meters/second²,
- The length of the pendulum, [tex]\( L = 1.8 \)[/tex] meters,
we substitute these values into the formula:
[tex]\[ T = 2 \pi \sqrt{\frac{1.8}{3.69}} \][/tex]
Now we perform the calculation step-by-step:
1. Calculate the division inside the square root:
[tex]\[ \frac{1.8}{3.69} \approx 0.4878 \][/tex]
2. Calculate the square root of the result:
[tex]\[ \sqrt{0.4878} \approx 0.6984 \][/tex]
3. Multiply this value by [tex]\( 2 \pi \)[/tex]:
[tex]\[ T = 2 \times 3.14159 \times 0.6984 \approx 4.388 \][/tex]
Thus, the period of the pendulum is approximately 4.388 seconds.
Next, we compare this calculated period to the given options to find the closest match:
- 3.9 seconds,
- 3.2 seconds,
- 0.87 seconds,
- 5.2 seconds,
- 4.4 seconds.
The closest option to 4.388 seconds is 4.4 seconds.
Therefore, the correct answer is:
○ E. 4.4 seconds
