Theory of Machine
Which is the false statement about the properties of instantaneous center?

The double center can be denoted either by O2 or O12, but proper selection should be made
At the instantaneous center of rotation, one rigid link rotates instantaneously relative to another for the configuration of mechanism considered
The two rigid links which have no linear velocity relative to each other at this center have the same linear velocity to the third rigid link
The two rigid links have no linear velocities relative to each other at the instantaneous center

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Theory of Machine
Lower pairs are those which have

Elements of pairs not held together mechanically
Point or line contact between the two elements when in motion
Surface contact between the two elements when in motion
Two elements that permit relative motion

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

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