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 $\frac{1}{2}k{x}^2$. The possible cases are

• A. The spring was initially compressed by a distance x and was finally in its natural length
• B. It was initially stretched by a distance x and finally was 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 a stretched position

Answer 1

Answer: (A), (B)

The correct options are
A

The spring was initially compressed by a distance x and was finally in its natural length

B

It was initially stretched by a distance x and finally was in its natural length

If the work done is positive this implied that the spring must have applied a force along the direction of

displacement.

From the options, only options (a) and (b) describe cases where, the spring applies a force along the

direction of displacement.