A student uses a simple pendulum of exactly `1m` length to determine `g`, the acceleration due ti gravity. He uses a stop watch with the least count of `1sec` for this and record `40 seconds` for `20` oscillations for this observation, which of the following statement `(s) is (are)` true?

Options

A. Error `DeltaT` in measuring T, the time period, is 0.05 seconds.
B. Error `DeltaT` in measuring T, the time period, is 1 second.
C. Percentage error in the determination of g is 5%.
D. Both a and c

Explanation

To determine the true statements regarding the measurement of acceleration due to gravity (g) using a simple pendulum, we will follow these steps:

### Step 1: Calculate the time for one oscillation
The student recorded a total time of 40 seconds for 20 oscillations. To find the time for one oscillation (T), we divide the total time by the number of oscillations.

\[ T = \frac{\text{Total Time}}{\text{Number of Oscillations}} = \frac{40 \text{ seconds}}{20} = 2 \text{ seconds} \]

### Step 2: Determine the least count of the stopwatch
The least count of the stopwatch is given as 1 second. This means the smallest time interval that can be accurately measured is 1 second.

### Step 3: Calculate the error in measuring time (Δt)
Since the least count is 1 second, the possible error in measuring time for one oscillation can be calculated as:

\[ \Delta t = \frac{\text{Least Count}}{2} = \frac{1 \text{ second}}{2} = 0.5 \text{ seconds} \]

### Step 4: Calculate the relative error in time measurement
The relative error in the time measurement can be calculated using the formula:

\[ \frac{\Delta t}{T} = \frac{0.5 \text{ seconds}}{2 \text{ seconds}} = 0.25 \]

### Step 5: Calculate the percentage error in time measurement
To express the relative error as a percentage, we multiply by 100:

\[ \text{Percentage Error in Time} = \frac{\Delta t}{T} \times 100 = 0.25 \times 100 = 25\% \]

### Step 6: Calculate the error in determining g (Δg)
The formula for the error in determining g is given by:

\[ \frac{\Delta g}{g} = 2 \frac{\Delta t}{T} \]

Substituting the values we have:

\[ \frac{\Delta g}{g} = 2 \times 0.25 = 0.5 \]

### Step 7: Calculate the percentage error in g
To find the percentage error in g, we multiply by 100:

\[ \text{Percentage Error in g} = 0.5 \times 100 = 50\% \]

### Conclusion
Based on the calculations, we can conclude that the percentage error in measuring g is 50%. Therefore, the true statements regarding the measurements and their errors can be identified based on this analysis.