A particle of mass $1$ kg is attached to one end of a spring having stiffness of $125$ $\mathrm{N} / \mathrm{m}$. The free length of the spring is $100$ mm . The system is rotated about the other end of the spring at a uniform angular velocity of $5 \mathrm{rad} / \mathrm{s}$. Ignore gravity and consider that the elongation of the spring may be comparable to the free length of the spring. The elongation of the spring $\text{(in mm , rounded off to the nearest integer)}$ is ____________.
