Question

If a spring of stiffness k is cut into two parts A and B of length La and Lb = 2:3, then the stiffness of spring A is ? [AIEEE 2011]​

Answer 1

A spring is cut into two parts of length La and Lb

Also given that La:Lb=2:3

If the length of spring is L , then La = 2L/5

And length of B , Lb= 3L/5

We know, for spring force , spring constant or stiffness of spring is inversely proportional to length of spring .

e.g.,Kα 1/L

If intial spring constant is k then,

kL=KaLa=KbLb

Then,Ka= k/(2/5) = 5k/2

And Kb= k/(3l/5) = 5k/3

Hence, stiffness of A is given by 5k/2.

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Answer 2

Explanation :- As we know that ,

• F = -kx [in spring]
• F ∝ 1/x ∝1/L

For spring , K ∝ 1/L

∵ Ka/K = L/La

But , L is cut into two parts La : Lb = 2:3

∴ Ka = (La + Lb) k/ La

⟹ Ka =( 2+3)K/2 = 5K/2 Answer