A spring force of constant k is cut into length of ratio 1:2:3. They are connected in series and the new force constant is k’. Then they are connected in parallel and the force constant is k”. Then k’: k” is:

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1:14

1:6

1:9

1:11

answer is D.

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Detailed Solution

Concept: We must first determine the stiffness of each spring individually before using the appropriate formula to determine the net stiffness of all the springs in order to calculate the net stiffness or force constant of springs. We shall divide the two situations after determining the net stiffness for each to arrive at the solution.
Assume that the spring has a total length of l and a spring constant of k. The length of the corresponding segments when the spring is divided into pieces with lengths 1:2:3 will be l/6, l/3, and l/2, respectively.
Even after the spring has been divided into several pieces, the product of the spring constant and its length is always constant. Kl is the result of the original spring's length and the spring constant. The many components of this product won't change.
Let spring constant of the springs of length l/6,l/3,l/2 be