The spring constant of spring `A` is twice the spring constant of spring `B`. Each of the spring is cut into two pieces. First piece of spring `A` is `(4//5)` of the total length. Second piece of spring `B` is `(5//6)` of its total length. Both springs are of equal lengh initially :

Options

A. the ratio of force constant of first piece of spring `B` to the first piece of spring `A` is `(12//5)`
B. the ratio of force constant of first piece of spring `B` to the first piece of spring `A` is `2`
C. the ratio of force constant of second piece of spring `A` to the first piece of spring `B` is `5//3`
D. the ratio of force constant of second piece of spring `A` to the first piece of spring `B` is `7//5`.

Answer

A, C

Explanation

`K_(A)=2K,K_(B)=K`
`(L_(A))_(1)=(4)/(5)L,(L_(A))_(2) =(L)/(5) ,(L_(B))_(1) =(L)/(6),(L_(B))_(2) =(5L)/(6)`
force constant `prop(1//5 "length")`
`(K_(A))_(1) =(5)/(4)(2K)=(5)/(2) K`,
`(K_(A))_(2) =5(2K) = 10 K`
`(K_(B))_(1) = 6(K)` and `(K_(B))_(2) = (6)/(5) (K)`.