$A$ rod of length $L$ revolves in a horizontal plane about an axis passing through its centre and perpendicular to its length. The angular velocity of the rod is $\omega$. If $A$ is the area of cross-section of the rod and $\rho$ is its density,then the rotational kinetic energy of the rod is

• A
  $\frac{1}{3} A L^3 \rho \omega^2$
• B
  $\frac{1}{2} A L^3 \rho \omega^2$
• C
  $\frac{1}{24} A L^3 \rho \omega^2$
• D
  $\frac{1}{18} A L^3 \rho \omega^2$