Question

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 Foece constant of

Answer 1

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

Force constant of larger piece is 1.5 K

Answer 2

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 x 1/ Length of the spring

K/K' = (2L/3)/L

K/K' = 2/3

K' = 3K/2

K' = 1.5 K