Two masses A and B having mass ma and mb, respectively, lying in the plane of the figure shown, are rigidly attached to a shaft which revolves about an axis through O perpendicular to the plane of the figure. The radii of rotation of the masses ma and mb are ra and rb, respectively. The angle between lines OA and OB is 90°. If ma=10 kg, mb=20 kg, ra=200 mm and rb=400 mm, then the balance mass to be placed at a radius of 200 mm is ___ kg (round off to two decimal places).
Explanation
Mass-radius products: ma·ra=10×0.2=2 kg·m (along OA), mb·rb=20×0.4=8 kg·m (along OB, perpendicular to OA). Resultant unbalance = √(2²+8²)=√68≈8.246 kg·m. Balance mass at r=0.2m: m_bal=8.246/0.2≈41.23 kg.
Source: GATE ME 2019 Session 2 (Set 3) (2019)
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