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A spring of length ℓ is cut into three segments in the ratio 1:2:3. Find the spring constant for each segment.

1. k₁ = 6k, k₂ = 3k, k₃ = 2k
2. k₁ = 2k, k₂ = 3k, k₃ = 6k
3. k₁ = 3k, k₂ = 6k, k₃ = 2k
4. k₁ = 6k, k₂ = 2k, k₃ = 3k

Correct answer: k₁ = 2k, k₂ = 3k, k₃ = 6k

Solution

The spring constant is inversely proportional to the length of the spring segment. Since the spring is divided into segments in the ratio 1:2:3, the lengths of the segments are ℓ/6, 2ℓ/6, and 3ℓ/6. The spring constants are k₁ = 6k, k₂ = 3k, and k₃ = 2k, respectively.

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