AIIMS 2017 Physics Simple Harmonic Motion MCQ Question

When a block of mass $m$ is pulled down by a distance $h$, the potential energy stored in the spring can be expressed using Hooke's Law, where the spring constant is $k$. The total potential energy is given by $U = \frac{1}{2} k x^2$, where $x$ is the extension of the spring. In this scenario, the extension $x$ can be derived from the equilibrium position and the additional displacement $h$, leading to the expression $U = \frac{mg}{k} \sqrt{1 + \frac{2hk}{mg}}$, which corresponds to option B.

Options A and C do not accurately represent the relationship between the gravitational force, spring constant, and displacement, while option D is incorrect as it does not provide a valid alternative. Understanding the interplay between gravitational potential energy and elastic potential energy is crucial in solving such problems.