Final answer:
The question requires the calculation of the percent change in tension in a string when the string's length is increased by 1%, considering the string is used to rotate a stone in a horizontal circle with a constant time period. The change in tension depends on the centripetal force, which is determined by the mass, velocity, and radius (length of string).
Step-by-step explanation:
The question concerns a stone being rotated in a horizontal circle with a constant tension and how the tension would change if the length of the string is increased. The relation between tension, period, and radius in circular motion can be determined by understanding that the centripetal force required for circular motion is provided by the tension in the string. Therefore, using the formula for centripetal force F = (m × v^2) / r, where m is the mass of the stone, v is its velocity, and r is the radius of the circular path, we can relate the tension T to the period T by considering that the velocity v is equal to the circumference of the circle (2πℓ) divided by the period (T), which gives us v = 2πℓ / T. Since we are asked about a small change in period rather than a precise value, we can use calculus or proportional reasoning.
For a small percentage increase in length ℓ, if the tension remains constant, the velocity decreases due to the increase in the length of the path while the period remains the same. However, since the tension is providing the centripetal force and the mass remains constant, a decrease in velocity would suggest a decrease in the required centripetal force, reflecting a decrease in tension. To find the exact percent change, we would need to use the centripetal force formula and the relationship between the velocity, the radius, and the period of rotation. The details of this calculation depend on the specifics of the rotation and the magnitude of the changes involved.