A simple spring has length l and force constant k. It is cut into two springs of length l1 and l2 such that l1=n l2(n= an integer). The force constant of the spring of length l2 is

Question

A simple spring has length l and force constant k. It is cut into two springs of length l1 and l2 such that l1=n l2(n= an integer). The force constant of the spring of length l2 is (A) k(1+n) (B) ((n+1) k/n) (C) k (D) k /(n+1)

Tardigrade Admin · Accepted Answer

Let k be the force constant of spring of length l2 . Since, l2=n l2, where n is an integer, so the spring is made of (n+1) equal parts in length, each of length l2. ∴ (1/k)=((n+1)/k) OR k=(n+1) k The spring of length l2(=n l2) will be equivalent to n spring connected in series where spring constant k'=(k/n)=((n+1) k/n)

Q. A simple spring has length $l$ and force constant $k$ . It is cut into two springs of length $l_{1}$ and $l_{2}$ such that $l_{1} = n l_{2} (n =$ an integer). The force constant of the spring of length $l_{2}$ is

k(1+n)

$\frac{( n + 1 ) k}{n}$

k

k /(n+1)

Q. A simple spring has length l and force constant k. It is cut into two springs of length l1​ and l2​ such that l1​=nl2​(n= an integer). The force constant of the spring of length l2​ is

k(1+n)

n(n+1)k​

k

k /(n+1)

Q. A simple spring has length $l$ and force constant $k$ . It is cut into two springs of length $l_{1}$ and $l_{2}$ such that $l_{1} = n l_{2} (n =$ an integer). The force constant of the spring of length $l_{2}$ is

$\frac{( n + 1 ) k}{n}$