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. `1:6`
B. `1:9`
C. `1:11`
D. `1:14`

Answer

C

Explanation

Pieces of spring after cutting the original spring will have new force constant
`K_(1)=6K,K_(2)=3K,K_(3)=2K`
as `Kprop(1)/("Length")`
In Parallel-
`K_("net")^(")=6K+2K+3K=11K`
In series-
`K_("net").=K` (as it will become original spring)
`thereforeK.:K"=1:11`.