In a certain observation we get `l =23.2 cm,r=1.32cm` and time taken for 20 oscillations was 20.0 sec. Taking `pi^2=10,`find the value of g in proper significant figures.

Explanation

To find the value of \( g \) based on the given data, we can follow these steps:

### Step 1: Calculate the Time Period
We are given that the time taken for 20 oscillations is 20.0 seconds. Therefore, the time period \( T \) for one oscillation can be calculated as:
\[ T = \frac{\text{Total time}}{\text{Number of oscillations}} = \frac{20.0 \, \text{s}}{20} = 1.00 \, \text{s} \]

### Step 2: Calculate the Effective Length
The effective length \( L \) of the pendulum is the sum of the length of the string and the radius of the bob. Given:
- Length of the string \( l = 23.2 \, \text{cm} \)
- Radius of the bob \( r = 1.32 \, \text{cm} \)

We can calculate \( L \) as:
\[ L = l + r = 23.2 \, \text{cm} + 1.32 \, \text{cm} = 24.52 \, \text{cm} \]
Rounding this to proper significant figures gives:
\[ L = 24.5 \, \text{cm} \]

### Step 3: Convert Length to Meters
Since we need to work in SI units, we convert \( L \) from centimeters to meters:
\[ L = 24.5 \, \text{cm} = 0.245 \, \text{m} \]

### Step 4: Use the Formula to Calculate \( g \)
The formula for the time period \( T \) of a pendulum is given by:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
Squaring both sides gives:
\[ T^2 = 4\pi^2 \frac{L}{g} \]
Rearranging this to solve for \( g \) gives:
\[ g = 4\pi^2 \frac{L}{T^2} \]

### Step 5: Substitute the Values
We are given \( \pi^2 = 10 \), \( L = 0.245 \, \text{m} \), and \( T = 1.00 \, \text{s} \). Substituting these values into the equation:
\[ g = 4 \times 10 \times \frac{0.245 \, \text{m}}{(1.00 \, \text{s})^2} \]
\[ g = 40 \times 0.245 = 9.8 \, \text{m/s}^2 \]

### Step 6: Final Answer
Thus, the value of \( g \) is:
\[ g = 9.8 \, \text{m/s}^2 \]