The spring constant of a spring is k. If the spring is cut into two halves then the spring constant of one of the halves is:
Correct answer: C. 2k
- A. k + 2
- B. k/2
- C. 2k
- D. k
Explanation
According to Hooke's Law, the force exerted by a spring is given by F = -kx, where k is the spring constant and x is the displacement. The spring constant is a measure of the spring's stiffness. When a spring is cut into two equal halves, each half becomes stiffer because the same force is now applied over a shorter distance. Therefore, the spring constant of each half becomes twice the original, or 2k. The other options are incorrect because they do not accurately reflect this relationship. Option A incorrectly adds a constant, Option B incorrectly assumes the spring constant is halved, and Option D assumes the spring constant remains unchanged.
This question appeared on the ETEA MDCAT 2012 paper, which you can sit online with every answer explained.
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Deformation and elasticity describe how solids change shape or volume under an applied force and return to their original form when the force is removed. Work includes stress, strain, Hooke’s law, elastic limit, Young’s modulus and elastic potential energy, while elastic deformation must be distinguished from permanent plastic deformation.
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