A spring of force constant 15 N/m is cut into two pieces. If the ratio of their length is 1:3, then the force constant of smaller piece i $s____N/m$
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Question

A spring of force constant 15 N/m is cut into two pieces. If the ratio of their length is 1:3, then the force constant of smaller piece i s____N/m

G1 Physics · Accepted Answer

For a uniform spring, k ∝ 1/L. The original spring is divided in the length ratio 1:3. Therefore the smaller piece has length L/4. If the original force constant is k = 15 N/m, then k(small) = k(L/(L/4)) = 4k = 4×15 = 60 N/m. Correct option: C.