To solve this problem, we need to understand the relationship between the potential energy stored in a spring and the amount it is stretched.$\\$The potential energy $(U)$ stored in a spring is given by the formula:$\\ U = \frac{1}{2} k x^2 \\$where:$\\$• $k$ is the spring constant.$\\$• $x$ is the displacement from the equilibrium position.$\\$Given that when the spring is stretched by 2 cm, the potential energy is $U,$ we can write:$\\ U = \frac{1}{2} k (2)^2 \\$Now, we need to find the potential energy when the spring is stretched by 8 cm.$\\ U' = \frac{1}{2} k (8)^2 \\$Simplifying $U': \\ U' = \frac{1}{2} k \cdot 64 \\$We know from the initial condition that:$\\ U = \frac{1}{2} k \cdot 4 \\$Thus, $U'$ can be expressed in terms of $U: \\ U' = \frac{1}{2} k \cdot 64 = 16 \left(\frac{1}{2} k \cdot 4\right) = 16U \\$Therefore, the potential energy stored when the spring is stretched by 8 cm is $16U. \\$This corresponds to Option 4.