The time periods of two simple pendulums at a place are in the ratio 2:1. What will be the corresponding ratio of their lengths?

Explanation

To solve the problem, we need to find the ratio of the lengths of two simple pendulums given the ratio of their time periods. Here's a step-by-step solution:

### Step 1: Understand the relationship between time period and length
The time period \( T \) of a simple pendulum is given by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where \( L \) is the length of the pendulum and \( g \) is the acceleration due to gravity.
...