A spring of spring constant $k$ is cut into two equal halves. The spring constant of each half is now

The spring constant ($k$) of a spring is inversely proportional to its natural length ($L$). This relationship is expressed as:
$$k\propto \frac{1}{L}⟹k\cdot L=\text{constant}$$

When the spring is cut into two equal halves, the length of each individual piece becomes:

$$L^{\prime }=\frac{L}{2}$$

Let the new spring constant be $k^{\prime }$. Equating the initial and final states:

$$k^{\prime }\cdot L^{\prime }=k\cdot L$$

$$k^{\prime }\cdot \left(\frac{L}{2}\right)=k\cdot L$$

$$k^{\prime }=2k$$

Hence, cutting the spring into two equal halves doubles the stiffness or spring constant of each individual piece.