If a simple pendulum takes 40 seconds to complete 20 oscillations, then the time period of the simple pendulum is

Question

Accepted Answer

To determine the time period of a simple pendulum, we need to understand the relationship between the time taken for a certain number of oscillations and the time period. The time period (T) is defined as the time taken for one complete oscillation.

In this scenario, the pendulum takes 40 seconds to complete 20 oscillations. To find the time period, we divide the total time by the number of oscillations:

$$ T = \frac{\text{Total time for oscillations}}{\text{Number of oscillations}} $$

$$ T = \frac{40 \text{ seconds}}{20 \text{ oscillations}} $$

$$ T = 2 \text{ seconds} $$

Therefore, the time period of the simple pendulum is 2 seconds, which corresponds to Option 1.

**Explanation of why other options are incorrect:**

- **Option 2 (0.2 second):** This option suggests that the time period is 0.2 seconds. If this were true, then 20 oscillations would take $ 20 \times 0.2 = 4 $ seconds, which contradicts the given information that 20 oscillations take 40 seconds.

- **Option 3 (5 second):** This option suggests that the time period is 5 seconds. If this were true, then 20 oscillations would take $ 20 \times 5 = 100 $ seconds, which is again inconsistent with the given 40 seconds for 20 oscillations.

- **Option 4 (0.5 second):** This option suggests that the time period is 0.5 seconds. If this were true, then 20 oscillations would take $ 20 \times 0.5 = 10 $ seconds, which does not match the provided 40 seconds for 20 oscillations.

In conclusion, the only option that correctly matches the calculation based on the given data is Option 1, which states that the time period of the simple pendulum is 2 seconds.