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`

Answer

B

Explanation

As we know spring constant `kprop(1)/(l)`
Length of the spring segments `=(l)/(6),(l)/(3),(l)/(2)`
So spring constant for spring segments will be
`k_(1)=6k` `k_(2)=3k=2k`
So in parallel combination, `k"=k_(1)+k_(2)+k_(3)=11k`
in series combination, `(1)/(k')=(1)/(6k)+(1)/(3k)+(1)/(2k)`
Hence `k'=k`
So `k':K"=1:11`