The relationship between the force applied to a spring (F), the spring constant (k), and the stretch (x) of the spring is given by Hooke's Law, which states:
\[ F = k \cdot x \]
Rearranging this formula gives us the spring constant:
\[ k = \frac{F}{x} \]
Since all springs are stretched by the same mass, the force \( F \) is constant for all the springs. The spring constant \( k \) is inversely proportional to the stretch \( x \) when \( F \) is constant. Thus, the greater the stretch, the smaller the spring constant.
Let's analyze the stretches:
- Spring A stretches 25 cm
- Spring B stretches 10 cm
- Spring C stretches 100 cm
- Spring D stretches 1 cm
Out of these, Spring C stretches the most (100 cm), which will correspond to the smallest spring constant because it can be stretched more easily.
Thus, the spring with the smallest spring constant is:
C.