What type of graph do you expect between (i) L and T and (ii) L and T^2 ?

Explanation

To solve the question regarding the expected type of graphs between (i) L and T and (ii) L and T² for a simple pendulum, we can follow these steps:

### Step-by-Step Solution

1. **Understanding the Relationship**:
- The time period \( T \) of a simple pendulum is given by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where \( L \) is the length of the pendulum and \( g \) is the acceleration due to gravity.

2. **Graph between L and T**:
- Rearranging the formula, we can express \( T \) in terms of \( L \):
\[ T \propto \sqrt{L} \]
- This indicates that \( T \) is directly proportional to the square root of \( L \). Therefore, if we plot \( T \) on the y-axis and \( L \) on the x-axis, we expect a curve that rises but flattens out as \( L \) increases. This is because the relationship is not linear but rather a square root function.

3. **Graph between L and T²**:
- Squaring both sides of the original formula gives:
\[ T^2 = 4\pi^2 \frac{L}{g} \]
- From this equation, we can see that:
\[ T^2 \propto L \]
- This indicates that \( T^2 \) is directly proportional to \( L \). Therefore, if we plot \( T^2 \) on the y-axis and \( L \) on the x-axis, we expect a straight line that passes through the origin. The slope of this line will be \( \frac{4\pi^2}{g} \).

### Summary of Expected Graphs
- (i) The graph between \( L \) and \( T \) is a curve (specifically, a square root curve).
- (ii) The graph between \( L \) and \( T^2 \) is a straight line passing through the origin.