Final answer:
When the string of an object in circular motion is lengthened and its speed remains constant, the centripetal acceleration decreases because it is inversely proportional to the radius.
Step-by-step explanation:
If the string is lengthened while the speed of the object remains constant, the centripetal acceleration of the object will decrease. This is because centripetal acceleration is given by the formula a = v^2/r, where a is the centripetal acceleration, v is the speed of the object, and r is the radius of the circle (in this case, the length of the string).
Since the speed (v) remains constant and the radius (r) increases when the string is lengthened, centripetal acceleration is inversely proportional to the radius of curvature. Therefore, if the string is lengthened (radius increases), the centripetal acceleration decreases.