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$A$ thin rod $AB$ is sliding between two fixed right angled surfaces. At some instant its angular velocity is $ \omega $. If $I_x$ represent moment of inertia of the rod about an axis perpendicular to the plane and passing through the point $X$ ($A, B, C$ or $D$), the kinetic energy of the rod is

• A
  $\frac{1}{2} I_A \omega^2$ 
• B
  $\frac{1}{2} I_B \omega^2$ 
• C
  $\frac{1}{2} I_C \omega^2$ 
• ✓
  $\frac{1}{2} I_D \omega^2$