The least count of a stop watch is 0.2 s, The time of 20 oscillations of a pendulum is measured to be 25s. The percentage error in the time period is

Options

A. 0.16
B. `0.8%`
C. `1.8%`
D. `8%`

Answer

To find the percentage error in the time period of the pendulum, we can follow these steps:

### Step 1: Identify the given values
- Least count of the stopwatch (Δt) = 0.2 seconds
- Time for 20 oscillations (T_total) = 25 seconds

### Step 2: Calculate the time period (T) of one oscillation
The time period (T) for one oscillation can be calculated using the formula:
\[ T = \frac{T_{total}}{n} \]
where \( n \) is the number of oscillations.

Here, \( n = 20 \):
\[ T = \frac{25 \, \text{s}}{20} = 1.25 \, \text{s} \]

### Step 3: Calculate the percentage error in the time period
The formula for percentage error is given by:
\[ \text{Percentage Error} = \left( \frac{\Delta t}{T} \right) \times 100 \]

Substituting the values we have:
\[ \text{Percentage Error} = \left( \frac{0.2 \, \text{s}}{1.25 \, \text{s}} \right) \times 100 \]

### Step 4: Perform the calculation
Calculating the fraction:
\[ \frac{0.2}{1.25} = 0.16 \]

Now, multiplying by 100 to get the percentage:
\[ \text{Percentage Error} = 0.16 \times 100 = 16\% \]

### Final Answer
The percentage error in the time period is **16%**.

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