Theory of Machine
The velocity of piston in a reciprocating steam engine is given by (where ω = Angular velocity of crank, r = Radius of crank pin circle, θ = Angle turned by crank from inner dead center, and n = Ratio of length of connecting rod to the radius of crank)

ω²r [cos θ + (cos 2θ/n)]
ωr [sin θ + (sin 2θ/n)]
ω²r [sin θ + (sin 2θ/n)]
ωr [cos θ + (cos 2θ/n)]

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Theory of Machine
Which of the following property of the instantaneous center is correct?

The two rigid links have no linear velocity relative to each other at the instantaneous centre.
The velocity of the instantaneous centre relative to any third rigid link is same whether the instantaneous centre is regarded as a point on the first rigid link or on the second rigid link.
All of these
A rigid link rotates instantaneously relative to another link at the instantaneous centre for the configuration of the mechanism considered.

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Theory of Machine
Which of the following statement is correct as regard to the difference between a machine and a structure?

A machine transforms the available energy into some useful work, whereas in a structure no energy is transformed into useful work
The parts of a machine move relative to one another, whereas the members of a structure do not move relative to one another
The links of a machine may transmit both power and motion, whereas the members of a structure transmit forces only
All of these

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