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. `((n+1)/(n))K`
B. K
C. `(K)/(n+1)`
D. K(1+n)

Answer

A

Explanation

Given that `l_(1)=nl_(2) therefore l =l_(1)+l_(2)=nl_(2)+l_(2)=(n+1)l_(2)`
but the spring constant `K prop (1)/(l)`.
If `K_(1)` is the spring constant of the part of length `l_(1)`,
then `(K_(1))/(K)=(l)/(l_(1))=((n+1)l_(2))/(nl_(2))=(n+1)/(n)`
`therefore K_(1)=((n+1)/(n))K`