Theory of Machine
In a reciprocating steam engine, when the crank has turned from inner dead centre through an angle θ, the angular velocity of the connecting rod is given by

ω cosθ/(n² - cos²θ)1/2
ω sinθ/(n² - cos²θ)1/2
ω cosθ/(n² - sin²θ)1/2
ω sinθ/(n² - sin²θ)1/2

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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?

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

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Theory of Machine
The steering of a ship means

None of these
Turning of a complete ship in a curve towards right or left, while it moves forward
Movement of a complete ship up and down in vertical plane about transverse axis
Rolling of a complete ship sideways

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Theory of Machine
For an isochronous Hartnell governor (where r₁ and r₂ = Maximum and minimum radius of rotation of balls respectively, S₁ and S₂ = Maximum and minimum force exerted on the sleeve respectively, and M = Mass on the sleeve)

S₁/S₂ = r₁/r₂
S₂/S₁ = r₁/r₂
(m.g + S₁)/(m.g + S₂) = r₁/r₂
(m.g - S₁)/(m.g - S₂) = r₂/r₁

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