GATE 2019 ME (ME2) – Question 48
Masses A and B are rigidly attached to a shaft rotating about O normal to the figure. Their radii OA and OB are at 90°. With mA = 10 kg, mB = 20 kg, rA = 200 mm and rB = 400 mm, find balance mass at radius 200 mm (kg), to two decimal places.
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Correct answer: 41 to 42
Explanation
The perpendicular unbalance vectors have magnitudes $m_Ar_A=2$ and $m_Br_B=8$ kg·m. Their resultant is $\sqrt{2^2+8^2}=8.24621$ kg·m. Balance mass at radius 0.2 m is $8.24621/0.2=\mathbf{41.23}$ kg, placed opposite the resultant.