I understand that you're having a bit of trouble determining the correct formula for centripetal force in uniform circular motion. Let's take a step back and review the key concepts again.

As we discussed earlier, centripetal force is necessary to keep an object moving in a circular path. It's directed towards the center of the circle and depends on the mass of the object, its velocity, and the radius of the circle.

To approach this question, let's analyze the relationship between these variables. We know that centripetal force is directly proportional to the mass of the object and the square of its velocity. This means that as the mass or velocity increases, the centripetal force also increases.

On the other hand, the centripetal force is inversely proportional to the radius of the circle. This means that as the radius increases, the centripetal force decreases.

Now, let's examine the options provided. We have four different formulas, each with a unique combination of variables. To determine which one is correct, we need to carefully consider the relationships between the variables.

One way to approach this is to think about the units of each variable. For example, what are the units of mass, velocity, and radius? How do these units relate to the unit of force?

Another strategy is to consider the physical meaning of each variable. What happens to the centripetal force when the mass of the object increases or decreases? What happens when the velocity increases or decreases?

By carefully analyzing the relationships between the variables and considering the physical meaning of each option, you should be able to narrow down the possibilities and make an informed decision.

Remember, the goal is not just to choose the correct option, but to understand the underlying principles and concepts that govern uniform circular motion. Take your time, and think critically about each option.

Additionally, it might be helpful to think about real-world examples of uniform circular motion, such as a car turning a corner or a satellite orbiting the Earth. How do the centripetal forces operate in these scenarios? What factors affect the magnitude of the centripetal force?

By combining your understanding of the concepts with your analysis of the options, you should be able to make a confident decision. Do you want to discuss any of the specific options in more detail or explore more concepts related to uniform circular motion?