Question

A uniform springs of force constant S is cut into two pieces whose length are in the ratio of 1:3 calculate the force constant of each place

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