CTET Paper II (Mathematics and Science) 20 Aug 2023 Solved Paper

Concept:Potential energy of a spring comes from two sources: elastic energy due to deformation (compression or extension) and gravitational energy due to height above the ground. The least potential energy occurs when both are zero.Explanation:The elastic potential energy stored in a spring is given by $PE_{\text{elastic}} = \frac{1}{2} k x^2$, where $x$ is the displacement from the natural length.Gravitational potential energy is $PE_{\text{gravity}} = mgh$, where $h$ is the height above the ground.- Option A: Spring is neither compressed nor pulled out and lies on the ground. Here $x = 0$ and $h = 0$, so both energies are zero. Total potential energy is 0.- Option B: Spring compressed to minimum but on ground. $x \neq 0$, so elastic energy is positive. Gravitational energy is zero. Total > 0.- Option C: Compressed to minimum and placed at height. Both $x \neq 0$ and $h > 0$, so both energies are positive. Total > 0.- Option D: Pulled out to maximum and placed at height. $x \neq 0$ and $h > 0$, again positive total energy.Thus, option A gives the least potential energy.Answer:Option A: The spring is neither compressed nor pulled out and is lying on the ground.