Answer & Solution
Answer: Option A
Solution:
When comparing the deflection of two springs with different mean diameters, we use the formula:
$$\left( \frac{\text{Deflection of Spring B}}{\text{Deflection of Spring A}} \right) = \left( \frac{\text{Mean Diameter of Spring A}}{\text{Mean Diameter of Spring B}} \right)^3$$
Given that spring 'A' has a mean diameter of 50 mm and spring 'B' has a mean diameter of 25 mm:
$$\left( \frac{50}{25} \right)^3 = 2^3 = 8$$
This implies that the deflection of spring 'B' is one-eighth $$ \frac{1}{8} $$ of the deflection of spring 'A'.
Hence, the correct answer is:
Option A: One-eighth
