A simple spring has length l and force constant K. It is cut into two springs of lengths `l_(1) "and" l_(2)` such that `l_(1) = n l_(2)` (n = an integer). The force constant of spring of length `l_(1)` is

Options

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

Answer

A

Explanation

Let k be the force constant of spring of length `l_(2)`. Since, `l_(2) = nI_(2)`, where n is an integer,
`because" "l_(1)+l_(2)=l or nl_(2) + l_(2) = l`
`therefore" "l_(2)=(l)/((n+1))" "because" "k_(1)l_(1)=k_(2)l_(2)`
`therefore" "k_(2)l_(2)="k l"`
`therefore" "k_(2)=kl//l_(2)=kl//(n+1)` pulting the value of `l_(2)`
`= (n+1)k`