A spring, having spring constant k when loaded with mass m, is cut into two equal parts. One of the parts is loaded with the same mass m again. What will be its new spring constant?

When a spring of constant k is cut into two equal parts, each part becomes stiffer because the same force causes a greater displacement in a shorter length. The spring constant of each half is given by k’ = 2k. This means that when one of the halves is loaded with the same mass m, it will exhibit double the stiffness compared to the original full-length spring. The reason for this is that the force-displacement relationship is inversely proportional to the length of the spring.

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