While determining the value of `g` using simple pendulum, we plot a graph between `l` and `T^(2)` which is

Options

A. a straight line
B. a parabola
C. an ellipse
D. a circle

Answer

To determine the value of `g` using a simple pendulum, we can analyze the relationship between the length of the pendulum (`l`) and the square of the period of oscillation (`T²`). The following steps outline how we arrive at the conclusion that the graph between `l` and `T²` is a straight line:

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The period `T` of a simple pendulum is given by the formula:
\[ T = 2\pi \sqrt{\frac{l}{g}} \]
Squaring both sides, we get:
\[ T^2 = 4\pi^2 \frac{l}{g} \]

2. **Rearranging the Equation**:
Rearranging the equation gives:
\[ T^2 = \frac{4\pi^2}{g} l \]
This shows that `T²` is directly proportional to `l`.

3. **Identifying the Form of the Equation**:
The equation can be expressed in the form of `y = mx + c`, where:
- \( y = T^2 \)
- \( x = l \)
- \( m = \frac{4\pi^2}{g} \) (the slope)
- \( c = 0 \) (the y-intercept)

4. **Conclusion about the Graph**:
Since the relationship between `T²` and `l` is linear (i.e., it can be expressed as `T² = ml + 0`), the graph of `T²` versus `l` will be a straight line.

### Final Answer:
The graph between `l` and `T²` is a **straight line**.

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