Question

A spring has length \(l\) and force constant \(k\). It is cut into 2 springs of length \(l_{1}\) and \(l_{2}\) such that \(l_{1}=nl_{2}\) (\(n\)=an integer). The force constant of the spring of length \(l_{2}\) is \(\left(k\propto \frac{1}{l}\right)\)

• A. \(k(n+1)\)
• B. \((n+1)\frac{k}{n}\)
• C. \(k\)
• D. \(\frac{k}{(n+1)}\)

Hint:

The force constant of a spring is inversely proportional to its length. Express l2 in terms of the total length.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
The force constant of a spring is inversely proportional to its length, so \(kl=\text{constant}\).

Step 2: Lengths After Cutting
The total length is \(l=l_1+l_2=nl_2+l_2=(n+1)l_2\).

Step 3: Apply the Proportion
For the piece of length \(l_2\), \(k_2l_2=kl\).

Step 4: Solve
\(k_2=\dfrac{k(n+1)l_2}{l_2}=k(n+1)\).

Final Answer:
The force constant of the spring of length l2 is k(n+1). \[ \boxed{\text{(A) }k(n+1)} \]