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A spring of force constant k is cut into two pieces, such that one piece is double the length of the other. Then the long piece will have a force constant of ___________

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A spring of force constant k is cut into two pieces, such that one piece is double the length of the other. Then the long piece will have a force constant of ___________

(a) (2/3) k

(b) (3/2) k

(c) 3k

(d) 6k

I have been asked this question in examination.

Question is taken from Harmonic Motion in portion Oscillations of Engineering Physics I

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The correct choice is (b) (3/2) k

The best I can explain: Force constant, k = F/x

The length of the long piece is 2x/3

So, its force constant is

k^‘=F/(2x/3)=3F/2x=3/2×k.

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