Answer :
Answer:
In this case, we can see that l1 is less than l2.
Therefore, the correct answer is: c) l1 < l2
Explanation:
The relationship between the length of a pendulum and its period can be determined by the formula for the period of a pendulum:
1. The period (T) of a pendulum is directly proportional to the square root of the length of the pendulum (l). Mathematically, this relationship is represented as T ∝ √l.
2. Given that the period of the pendulum is 2.5 seconds when the length is l1 and 3.5 seconds when the length is l2, we can set up the following proportions:
T1 = 2.5 seconds and l1
T2 = 3.5 seconds and l2
3. Using the formula T ∝ √l, we can write the proportions as:
T1 / T2 = √(l1 / l2)
4. Substitute the given values into the equation:
2.5 / 3.5 = √(l1 / l2)
5. Simplify the equation:
2.5 / 3.5 = √(l1 / l2)
0.714 ≈ √(l1 / l2)
6. Square both sides of the equation to solve for the relationship between l1 and l2:
0.714^2 = l1 / l2
0.51 ≈ l1 / l2
7. From the relationship 0.51 ≈ l1 / l2, we can see that l1 is less than l2. Therefore, the correct answer is: c) l1 < l2
