Question

The spring will have maximum potential energy when
A) it is pulled out
B) it is compresses
C) both (A) and (B)
D) neither (A) nor (B)

Answer 1

Hint The potential energy of a spring is associated with its tendency to return to its original position. It will have maximum potential energy when it is the farthest from its original position.
$\Rightarrow U = \dfrac{1}{2}k{x^2}$ where $U$ is the potential energy stored in the spring, $k$ is the spring constant, $x$ is the displacement of the end of the spring from its rest position.

Complete step by step answer
The potential energy of the spring is calculated using the formula $U = \dfrac{1}{2}k{x^2}$ where $x$ is the displacement of the end of the spring from its rest position. Since $k$ is a constant, the potential energy will only depend on the displacement of the particle.
In option (A), when the spring is pulled out, it will be the farthest from its rest position in one direction so $x$ will be maximum and the spring will have maximum potential energy so option (A) is correct.
In option (B), when the spring is compressed, it will again be displaced from its rest position $x$ will be maximum so the spring will have maximum potential energy and option (B) is also correct.
Since option (A) and (B) both are correct, option (C) is the correct option.

Note
Since the potential energy of the spring depends on the square of the displacement of the end of the spring from its rest position, regardless of which direction one end of the spring is displaced, i.e. positive or negative direction, the potential will increase as the spring moves from its original rest position.