Theory of Machine
A rigid body, under the action of external forces, can be replaced by two masses placed at a fixed distance apart. The two masses form an equivalent dynamical system, if

The center of gravity of the two masses coincides with that of the body
The sum of mass moment of inertia of the masses about their center of gravity is equal to the mass moment of inertia of the body
The sum of the two masses is equal to the total mass of body
All of these

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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

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

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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

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

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