Final answer:
To calculate the tension at the top of the circle, use the object's mass, the radius of the circle, and the time for one revolution to first find the speed. Then apply the formula T + mg = mv²/r, considering both the centripetal force requirement and the object's weight, to solve for the tension.
Step-by-step explanation:
To determine the tension in the string at the top of the circle for the 2.25 kg object, we must consider two forces acting on the object: the gravitational force (weight of the object) and the centripetal force needed to keep the object moving in a circle. The tension in the string must provide the centripetal force while also counteracting the object's weight. First, calculate the speed (v) of the object using the given radius (r) and time (T) for one revolution. Using the formula v = 2πr/T, find the speed. Then, use the formula for centripetal force Fc = mv²/r. At the top of the circle, the tension (T) plus the weight of the object (mg) must equal the centripetal force, so the formula is T + mg = mv²/r. With the values m = 2.25 kg, r = 0.89 m, and g = 9.81 m/s², and by substituting the calculated speed (v) into the formula, you can solve for the tension (T).