A spring has length'l' and spring constant 'k'. It is cut into two pieces of lengths `l_(1) and l_(2)` such that `l_(1)=nl_(2)`. The force constant of the spring of length `l_(1)` is

Options

A. `k(1+n)`
B. `k//n(1+n)`
C. k
D. `k//(n+1)`

Answer

A

Explanation

`l_(1)+l_(2)=l`
`therefore l=nl_(2)+l_(2)=l_(2)(n+1)`
`(F)/(l)=k and (F)/(l_(2))=k_(1)`
`therefore (k)/(k_(1))=(l_(2))/(l_(2)(n+1)) therefore k_(1)=(n+1)K`