Question

There are four springs stretched by the same mass. Spring A stretches 25 cm. Spring B stretches 10 cm. Spring C stretches 100 cm.
Spring D stretches 1 cm.
Which spring has the smallest spring constant?
A
B
C
D

Answer 1

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**.