Question

Choose the correct graph between time period \( T \) and length of pendulum \( l \).

• A. A
• B. B
• C. C
• D. D

Hint:

The time period of a simple pendulum is directly proportional to the square root of its length.

Answer 1

The Correct Option is D

Step 1: Recall the formula for the time period of a pendulum.
The time period \( T \) of a simple pendulum is given by: \[ T = 2 \pi \sqrt{\frac{l}{g}}, \] where \( l \) is the length of the pendulum and \( g \) is the acceleration due to gravity. Step 2: Analyze the relation.
From the equation, we can see that the time period \( T \) is proportional to \( \sqrt{l} \). Therefore, \( T^2 \propto l \), which implies \( \frac{1}{T^2} \propto \frac{1}{l} \). Final Answer: \[ \boxed{\frac{1}{T^2} \propto l}. \]