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A rigid body in the $\text{X-Y}$ plane consists of two point masses ($1$ $\text{kg}$ each) attached to the ends of two massless rods, each of $1$ $\text{cm}$ length, as shown in the figure. It rotates at $30$ $\text{RPM}$ counter-clockwise about the $Z$-axis passing through point $O$. A point mass of $\sqrt{2}$  $\text{kg}$, attached to one end of a third massless rod, is used for balancing the body by attaching the free end of the rod to point $O$. The length of the third rod is _______________ $\text{cm}$.

  1. $1$
  2. $\sqrt{2}$
  3. $1/\sqrt{2}$
  4. $1/2\sqrt{2}$


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