The unit of the force constant k of a spring is
- A.N-m
- B.N/m
- C.N-m²
- D.N/m²
Correct answer
Explanation
The correct answer is B, N/m. The spring constant is force divided by extension, so its SI unit is newton per metre.
Hooke's law says that, within the elastic limit, the restoring force of a spring is proportional to how far it is stretched or compressed: F = −kx. Rearranged, k = F/x, which is newtons divided by metres. A stiff spring has a large k and needs a big force for a small stretch; a soft spring has a small k. The constant also fixes how fast a mass on the spring oscillates, since the time period is T = 2π√(m/k).
A is wrong: newton-metre is the unit of torque, and of work as the joule.
C is wrong: N·m² is not the unit of any spring property; it appears in quantities such as the gravitational constant with kg².
D is wrong: N/m² (pascal) is the unit of pressure and stress, not of the spring constant.
Exam tip: spring constant in N/m; surface tension also in N/m; stress and pressure in N/m² (Pa); torque in N·m.
Practice Questions
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