The spring constant (k) of a spring can be calculated using Hooke's Law, which states that the force (F) applied to a spring is directly proportional to the displacement (x) it causes, mathematically represented as:
\[ F = kx \]
In this case, since all springs are stretched by the same mass, they are all experiencing the same force. Therefore, we can say:
\[ k \propto \frac{1}{x} \]
This means the spring constant is inversely proportional to the displacement. The smaller the displacement (stretch), the larger the spring constant.
Now, let's look at the stretches:
- Spring A stretches 25 cm (0.25 m)
- Spring B stretches 10 cm (0.10 m)
- Spring C stretches 100 cm (1.00 m)
- Spring D stretches 1 cm (0.01 m)
Among these, Spring D stretches the least (1 cm), which means it will have the largest spring constant.
Thus, the answer is:
D.
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