Question

Using a simple pendulum experiment $g$ is determined by measuring its time period $T$. Which of the following plots represent the correct relation between the pendulum length $L$ and time period $T$?

• A. A
• B. B
• C. C
• D. D

Hint:

In simple pendulum experiments, plotting $\dfrac{1}{T^2}$ vs $L$ gives an inverse curve, while plotting $T^2$ vs $L$ gives a straight line.

Answer 1

The Correct Option is D

The problem involves understanding the relationship between the length of a pendulum \(L\) and its time period \(T\). The time period \(T\) of a simple pendulum is given by the formula: 

\(T = 2\pi \sqrt{\frac{L}{g}}\)

Squaring both sides, we get:

\(T^2 = 4\pi^2 \frac{L}{g}\)

This can be rearranged to express as:

\(\frac{1}{T^2} = \frac{g}{4\pi^2} \cdot \frac{1}{L}\)

This expression shows that \(\frac{1}{T^2}\) is inversely proportional to \(L\). Therefore, the plot of \(\frac{1}{T^2}\) versus \(L\) should be a hyperbolic (curve downwards). Option D correctly represents this inverse relationship.

Hence, the correct answer is D.