The graph between the length and square of the period of a simple pendulum is a

Options

A. circle
B. parabola
C. straight line
D. hyperbola

Explanation

To determine the relationship between the length (l) of a simple pendulum and the square of its period (T²), we start with the formula for the period of a simple pendulum:

1. **Write the formula for the period of a simple pendulum:**
\[ T = 2\pi \sqrt{\frac{l}{g}} \]
where \( T \) is the period, \( l \) is the length of the pendulum, and \( g \) is the acceleration due to gravity.

2. **Square both sides of the equation:**
\[ T^2 = (2\pi)^2 \frac{l}{g} \]
This simplifies to:
\[ T^2 = \frac{4\pi^2}{g} l \]

3. **Rearrange the equation to express length (l) in terms of \( T^2 \):**
\[ l = \frac{g}{4\pi^2} T^2 \]
This shows that length \( l \) is directly proportional to the square of the period \( T^2 \).

4. **Identify the form of the equation:**
The equation \( l = m T^2 \) can be compared to the linear equation \( y = mx \), where:
- \( y \) is \( l \)
- \( x \) is \( T^2 \)
- \( m \) is the slope, which is \( \frac{g}{4\pi^2} \)

5. **Conclusion about the graph:**
Since the equation is in the form \( y = mx \), the graph of length \( l \) versus the square of the period \( T^2 \) will be a straight line passing through the origin.

### Final Answer:
The graph between the length and square of the period of a simple pendulum is a straight line passing through the origin.

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