All right. So for this problem, we have two pendulums ones on the planet Earth and ones on some unknown planet. And both have the same length string. However, they're on different planets, so they're experiencing different gravity's, and they both have separate periods. So the period of the pendulums on earth is 0.65 seconds in the period of the pendulums on the unknown, Planet P is equal to 0.862 seconds. And the first thing we have to answer is is the gravitational field on the unknown planet stronger or weaker than the gravitational field on Earth? So we're gonna look at the equation for the period of a pendulum is equal to pi times the square root of length of pendulum divide by the gravitational field of experiencing, and we're going to you analytically say All right, So if G is larger, then we're going to have a smaller period. Since she's in the denominator of this equation. If g of smaller, they won't have a larger period because in the nominee of the equation, there's an inverse law going on here. So then we're going to analyze the period of the pendulum on the Unknown Planet. We noticed that it's greater. It is greater than TCBY or he just read it like this mathematically. So if TCP is greater than TCBY, then Jesus Api. The gravity on the Unknown Planet must be lesser because there's an inverse law here. We state that the period of any pens alone is proportional to the inverse of the gravitational field with pendulum is experiencing. That's the first thing we ventured. We already know that G is going to be lesser on the Unknown Planet than it is gonna be on Earth simply due to this relation here. Now we just have to learn what is Guille neo known planet? Well, we can say we can compare the two periods and thusly compare the two gravity's through their equations. So let's do that. Let's say T sub e for the period of the pendulum Earth divided by the period of the pendulum on the Unknown Planet, it's simply going to be equal to their individual equations. So it's going to be two pi times the square root of the length of the pendulum. And remember, the length of the pendulum doesn't change that the same length pendulum on both Earth and the Unknown Planet divided by the gravity on earth. And this whole product is going to be divided by the equation for the period on the Unknown planet two pi times square, root of the length divided by the gravity on the Unknown Planet. All right, so what immediately cancels out here? The two pies cancel out so you can rewrite this and we can extend the square root to cover over this whole set of three fractions. If we do our fraction division correctly, we should notice that the else cancel this whole thing legal to the square root of geese API divided by gcb. All right, so because we have values for Tee Savi and TCP, we can plug them into this equation here and swear the whole equation today to get geese api Overdue city out of the square root. So it's plug in the values and then swear them. Let's say TV 0.65 This would be 0.65 divided by TCP, which is 0.862 We want to square this little thing and say that's equal to gee soapy, divided by gcb Now this is Multiply gcb over and evaluate this. If we evaluate this, it's going to be equal to 0.56 mine. And because we know the value of gcb to be 9.8, the gravity on Earth gravitational acceleration on earth 0.569 times 9.8 is equal to the gravitational acceleration on the planet peak. It's the gravitational acceleration. The Planet P must be equal to 5.57 meters per second squared.