A spring of force constant `k` is cut into lengths of ratio `1 : 2 : 3`. They are connected in series and the new force constant is k'. Then they are connected in parallel and force constant is k'. Then k' : k" is :

Options

A. `1 : 9`
B. `1 : 11`
C. `1 : 14`
D. `1 : 16`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Determine the lengths of the springs
Given that the spring is cut into lengths in the ratio of 1:2:3, we can denote the lengths as:
- Let the length of the first spring \( L_1 = x \)
- Let the length of the second spring \( L_2 = 2x \)
- Let the length of the third spring \( L_3 = 3x \)

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