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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Solution

Length of the spring = L
Force constant of spring = K

Ratio in which spring is cut = 1 : 2
Length of larger piece = 2L / (2 + 1) = 2L/3
Force constant of larger piece = K’

Force constant ∝ 1 / Length of the spring

K / K’ = (2L / 3) / L
K / K’ = 2 / 3
K’ = 3K / 2
K’ = 1.5 K
Then the long piece will have a force constant of 1.5 k

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