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

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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/4
Become equal to R/2
Become equal to 2R

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Theory of Machine
A thin circular disc is rolling with a uniform linear speed, along a straight path on a plane surface. Which of the following statement is correct in this regard?

All points of the disc have the same velocity
The centre of the disc has centrifugal acceleration
The centre of the disc has zero acceleration
The point on the disc making contact with the plane surface has zero acceleration

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