Which of the following is the correct SI unit for the spring constant $k$ in Hooke's Law?

• A. $\frac{N}{m}$
• B. $\mathrm{kg}$
• C. $J$
• D. $m$

Answer: (A)

Verified step by step guidance

1. Recall Hooke's Law, which states that the force exerted by a spring is proportional to the displacement: \(F = -k x\), where \(F\) is the force, \(k\) is the spring constant, and \(x\) is the displacement.
2. Identify the SI unit of force \(F\), which is the newton (N), and the SI unit of displacement \(x\), which is the meter (m).
3. Rearrange Hooke's Law to express the spring constant: \(k = \frac{F}{x}\).
4. Substitute the units into the expression for \(k\): since \(F\) is in newtons (N) and \(x\) is in meters (m), the unit of \(k\) is \(\frac{\text{N}}{\text{m}}\).
5. Conclude that the correct SI unit for the spring constant \(k\) is newtons per meter, \(\frac{\text{N}}{\text{m}}\).