QJEEM23Ph4497: JEE Main 2023 Physics - Class 11 JEEM23Ph4497 Solution: Choose the correct length (L) versus square of the time period…

The relationship between the length of a pendulum and its period is given by the equation:

$$T=2\pi \sqrt{\frac{L}{g}}$$

$$\Rightarrow$$ $${\mathrm{T}}^2=\frac{4{\pi }^2}{g}\cdot \mathrm{L}$$

where T is the period of the pendulum, g is the acceleration due to gravity, and L is the length of the pendulum. This equation shows that the square of the period is directly proportional to the length of the pendulum.

Therefore, a graph of T² vs. L will be a straight line with a positive slope, passing through the origin. The slope of the line will be equal to $$\frac{4{\pi }^2}{g}$$, and its intercept will be zero.

Note : Graph of T vs. L will be a parabola not T² vs. L as in equation of parabola y² = 4ax, graph of y vs. x is parabola not y² vs. x. As y² vs. x is a straight line.