GATE 2016 ME (ME3) – Question 46
Two masses m are attached to opposite sides of a rigid rotating shaft in the vertical plane. Another pair of equal masses m1 is attached to the opposite sides of the shaft in the vertical plane as shown in figure. Consider m = 1 kg, e = 50 mm, e1 = 20 mm, b = 0.3 m, a = 2 m and a1 = 2.5 m. For the system to be dynamically balanced, m1 should be ________ kg.
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Show answer and explanation
Correct answer: 1.9 to 2.1
Explanation
The opposite members of each equal pair cancel their net centrifugal forces. Couple balance therefore requires m e a=m₁e₁a₁; the common factorω² cancels. Substituting1×0.05×2=m₁×0.02×2.5 gives **m₁=2kg**. The offset b does not affect a balanced force pair’s couple.