Which of the following graph depicts spring constant `k` versus length `l` of the spring correctly

Options

A. a straight line
B. an ellipse
C. a parabola
D. a hyperbola

Answer

D

Explanation

For the spring `K=(F)/(x)` where x is the increase in length for the applied force F.
But `x prop L` (the original length)
`therefore K prop (1)/(L)`
`therefore` The nature of the graph is a hyperbola.
[Similar to `P prop (1)/(V)` or frequency `n prop (1)/(l)`]