AIIMS 2019 Physics Spring Systems MCQ Question

Option A is correct because it represents the formula for calculating the equivalent spring constant $K_{eq}$ for two springs $K_1$ and $K_2$ arranged in series, where $K_{eq} = \frac{K_1 K_2}{K_1 + K_2}$. This formula arises from the principle that the total extension in a series arrangement is the sum of the extensions in each spring, leading to the relationship between the forces and displacements.

Option B incorrectly suggests that the equivalent spring constant is simply the product of the two spring constants, which does not account for the series configuration. Option C misrepresents the relationship by incorrectly placing the product in the numerator and denominator, while option D describes the formula for springs in parallel, not in series. Understanding these distinctions is crucial for correctly applying Hooke's law in different configurations.