Final answer:
Cutting a spring in two equal parts results in each piece having double the spring constant, but the reason given is not correct as the spring constant depends on several factors, not just length. The correct answer is A is true and R is false.
Step-by-step explanation:
The correct answer is A is true and R is false. When a spring is cut into two equal parts, each piece becomes stiffer because the spring constant, often denoted by 'k', is indeed inversely proportional to the number of coils but not directly to the length of the spring.
This is because the spring constant is more accurately related to the spring's dimensional properties, such as coil thickness, material, and coil diameter, along with how tightly the coils are wound. If a single long spring is cut into two, each half contains half the number of coils, effectively doubling the spring constant. However, the statement that spring constant is inversely proportional to the length of the spring is not exactly true — it assumes that all other factors remain constant which isn't always the case in real-world applications.
The statement A is true, but the reason R is not correct. When a spring is cut into two equal parts, the spring constant of each piece remains the same, not doubled.
The spring constant depends on the material and physical properties of the spring, such as its shape and dimensions, rather than just the length. Therefore, neither A nor R can be considered as the correct explanation of the other.
The correct answer is A is true and R is false.