Project ForgeA 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, perpendicular to each other as shown in the figure. It rotates at 30 RPM counter-clockwise about the Z-axis passing through point O. A point mass of √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.
- 1
- B√2
- C1/√2
- D1/2√2
Explanation
For static balance, the mass moment vectors must sum to zero: Σmᵢrᵢ=0. The two 1 kg masses (each at 1 cm, perpendicular to each other) have mass moments of magnitude 1 kg·cm each, at 90° to one another, so their resultant has magnitude √(1²+1²)=√2 kg·cm. The balancing mass (√2 kg at radius r3) must exactly cancel this: √2×r3=√2, giving r3=1 cm.
Source: GATE ME 2022 Session 2 (ME-2) (2022)
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