List of top Applied Mechanics and Design Questions on Balancing of reciprocating and rotating masses asked in GATE ME

A rigid body in the X–Y plane consists of two point masses (1 kg each) attached to the ends of two massless rods, each of 1 cm length, as shown in the figure. It rotates at 30 RPM counter-clockwise about the Z-axis passing through point O. A point mass of $\sqrt{2$ 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 ________________ cm.}