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Mechanical Properties Of Fluids

Question
CBSEENPH11019263

A spring of constant k is divided into two parts of equal length. What is the spring constant of either part?

Solution
Let a spring AC of spring constant K be divided into two equal parts AB and BC.
We have AB = BC, therefore spring constant of each part will be the same and let it be K'.
Suppose, spring AC consists of two springs AB and BC connected in series. 
 
The spring constant is given by, 
space space space space space space 1 over straight K space equals space fraction numerator 1 over denominator K apostrophe end fraction plus fraction numerator 1 over denominator K apostrophe end fraction space equals space 2 over K to the power of apostrophe space

rightwards double arrow space space space K apostrophe space equals space 2 K
i.e. spring constant of both the parts is 2K.