Spring cut into parts – Rankers Physics

Motion of Connected Bodies: Practice Problem & Solution

A spring of length \(L\) and spring constant \(K\) is cut into two parts of length \(\frac{L}{3}\) and \(\frac{2L}{3}\), then the spring constant of each part will be
\(3K, \frac{3K}{2}\)
\(2K, \frac{2K}{3}\)
\(K, \frac{K}{3}\)
\(K, K\)

Solution Explained:

To solve this problem, we apply the core principles of Motion of Connected Bodies. Understanding the underlying formula is key to arriving at the correct answer below:

The spring constant is inversely proportional to the length of the spring: \(k \propto 1/l\). For lengths \(L_1 = L/3\) and \(L_2 = 2L/3\), the spring constants are \(k_1 = 3K\) and \(k_2 = 1.5K = 3K/2\).

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