Barron's 2nd Edition DT Q37

Barron's Book

37) This question asks us to find out the factor at which u need to stretch a spring to quadruple its initial potential energy. Let’s first make an original relation.

Where U is potential energy, k is spring constant, and x is spring displacement

Now, we need to look at how the spring stretches in order for the potential energy to quadruple.

Where U is potential energy, k is spring constant, and x is spring displacement

Answer: A