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(D) 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 and $x$ is the displa

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$25 U$

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(D) 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 and $x$ is the displacement.From this relation,we can see that $U \propto x^2$.Given the initial displacement $x_1 = 2 \ cm$ and initial energy $U_1 = U$.The new displacement is $x_2 = 10 \ cm$.Using the ratio method: $\frac{U_2}{U_1} = \left( \frac{x_2}{x_1} \right)^2$.Substituting the values: $\frac{U_2}{U} = \left( \frac{10 \ cm}{2 \ cm} \right)^2 = (5)^2 = 25$.Therefore,the new potential energy is $U_2 = 25 U$.

When a spring is stretched by $2 \ cm$,the potential energy stored is $U$. If it is stretched by $10 \ cm$,the potential energy stored will be:

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