$A$ particle of mass $m$ is fixed to one end of a light spring having force constant $k$ and unstretched length $\ell$. The other end is fixed. The system is given an angular speed $\omega$ about the fixed end of the spring such that it rotates in a circle in gravity-free space. Then the stretch in the spring is

• A
  $\frac{m \ell \omega^{2}}{k+m \omega^{2}}$
• B
  $\frac{m \ell \omega^{2}}{k-m \omega^{2}}$
• C
  $\frac{m \ell \omega^{2}}{k-m \omega}$
• D
  $\frac{m \ell \omega^{2}}{k+m \omega}$