Question

A spring is stretched twice its initial extension. Compared to its initial value, the potential energy ________.

• A. becomes four times
• B. is doubled
• C. is halved
• D. remains the same
• E. becomes zero

Hint:

Energy scales with the square of the displacement.

Answer 1

The Correct Option is A

Step 1: Concept
Elastic potential energy is $U = \frac{1}{2} k x^{2}$.

Step 2: Meaning
Potential energy is directly proportional to the square of the extension ($U \propto x^2$).

Step 3: Analysis
If $x$ is doubled ($x \to 2x$), then $U \to (2)^{2} U = 4U$.

Step 4: Conclusion
The potential energy becomes four times its initial value. Final Answer: (A)