Question

One end of a light spring of spring constant k is fixed to a wall and the other end is tied to a block placed on a smooth horizontal surface. In a displacement, the work done by the spring is $1/2k{x}^2$. The possible cases are

• A. the spring was initially compressed by a distance x, was finally in its natural length
• B. it was initially stretched by a distance x and was finally in its natural length
• C. it was initially in its natural length and finally in a compressed position
• D. It was initially in its natural length and finally in the stretched position

Answer 1

Answer: (A), (B)

the spring was initially compressed by a distance x, was finally in its natural length
it was initially stretched by a distance x and was finally in its natural length

Stored elastic potential energy of spring $=\frac{1}{2}k{x}^2$ where $x$ is compression or elongation of spring from its natural length. In this position the spring can do work on the block tied to it, which is equal to $\frac{1}{2}k{x}^2$, so both option (a) & b are correct.