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(D) The potential energy stored in a spring is given by $U = \frac{1}{2} k x^2$,where $k$ is the spring constant and $x$ is the displacement.This impl

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$36U$

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(D) The potential energy stored in a spring is given by $U = \frac{1}{2} k x^2$,where $k$ is the spring constant and $x$ is the displacement.This implies $U \propto x^2$.Initially,the displacement is $x_1 = 2 \, cm$,so $U = C(2)^2 = 4C$,where $C$ is a constant.When the spring is stretched by an additional $10 \, cm$,the new total displacement becomes $x_2 = 2 \, cm + 10 \, cm = 12 \, cm$.The new energy stored is $U' = C(12)^2 = 144C$.Taking the ratio of the new energy to the initial energy:$\frac{U'}{U} = \frac{144C}{4C} = 36$.Therefore,the new energy stored is $U' = 36U$.

In stretching a spring by $2 \, cm$,the energy stored is $U$. If the spring is stretched by an additional $10 \, cm$,the total energy stored will be:

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