Theory of Machine
A disturbing mass m₁ attached to the rotating shaft may be balanced by a single mass m₂ attached in the same plane of rotation as that of m₁, such that (where r₁ and r₂ are the radii of rotation of m₁ and m₂ respectively)

m₁ r₂ = m₂ r₁
m₁ r₁ = m₂ r₂
m₁ m₂ = r₁ r₂
None of these

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Theory of Machine
Two heavy rotating masses are connected by shafts of lengths l₁, l₂ and l₃ and the corresponding diameters are d₁, d₂ and d₃. This system is reduced to a torsionally equivalent system having uniform diameter d = d₁ of the shaft. The equivalent length of the shaft is

l₁ + l₂ + l₃
(l₁ + l₂ + l₃)/3
l = l₁ + l₂.(d₁/d₂)³ + l₂.(d₁/d₃)³
l = l₁ + l₂.(d₁/d₂)⁴ + l₃.(d₁/d₃)⁴

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Theory of Machine
A rotor which is balanced statically but not dynamically is supported on two bearings L apart and at high speed of the rotor, reaction on the left bearing is R. The right side of the bearing is shifted to a new position 2L apart from the left bearing. At the same rotor speed, dynamic reaction on the left bearing in the new arrangement will

Become equal to 2R
Become equal to R/4
Become equal to R/2
Remain same as before

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