A block of mass m is tied to one end of a string of length l, young's modulus Y and cross-sectional area A. The block is made to rotate in a horizontal circle of radius l with angular velocity $\omega$ in a gravity free space. If elongation of the wire is x, then elastic potential energy stored in the wire is

• A

  $\frac{1}{2}m{\omega }^{2}lx$

• B

  $\frac{m{\omega }^{2}lx}{4}$

• C

  $\frac{1}{2}m{\omega }^2{l}^2$

• D

  $\frac{1}{4}m{\omega }^2{l}^2$