In this question, we are asked to identify the correct graph representing the displacement of an object in uniform circular motion along the x-axis. Let`s analyze each option to determine the correct answer.

Option 1 (I): In this graph, the displacement starts at zero and increases with time until it reaches a maximum value, after which it decreases back to zero. This pattern corresponds to one complete revolution in circular motion. Therefore, option 1 correctly represents the displacement in uniform circular motion.

Option 2 (II): In this graph, the displacement starts at zero and remains constant throughout, indicating that the object is not moving. This contradicts the premise of uniform circular motion, where the object must have a changing displacement.

Option 3 (III): In this graph, the displacement starts at zero and gradually increases with time, but it does not reach a maximum value or decrease back to zero. This pattern is not consistent with the behavior of an object in uniform circular motion.

Option 4 (IV): In this graph, the displacement starts at a non-zero value and remains constant, indicating that the object is not changing its position. This contradicts the premise of uniform circular motion, where the object must have a changing displacement.

Therefore, option 1 is the only graph that