Question

A spring having a spring constant ${}^{\prime }{K}^{\prime }$ is loaded with a mass ${}^{\prime }{m}^{\prime }$. The spring is cut into two equal parts and one of these is loaded again with the same mass. The new spring constant is

• A. $K/2$
• B. $K$
• C. $2K$
• D. $K^2$

Answer 1

The correct option is C $2K$

It doubles. The easiest way to imagine this is by applying an equal force F to each end while the center remains unmoved. The spring constant is $k=\frac{F}{2x}$, where x is the distance each ends moves. Effectively, the spring compresses by a distance $2x$ overall. But now look at only the left half of the spring. The force F caused compression of $x$ only. The new spring constant for the half spring is, $\therefore$ $\frac{F}{x}=2k$