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Theory of Machine

Theory of Machine
In S.H.M., the velocity vector w.r.t. displacement vector

Are in phase
Lags by 90°
Leads by 90°
Leads by 180°

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Theory of Machine
The frictional torque transmitted in a flat pivot bearing, assuming uniform wear, is (Where μ = Coefficient of friction, W=Load over the bearing, R=Radius of bearing)

½μWR
²/₃ μWR
¾μWR
μwr

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Theory of Machine
The train value of a gear train is

Always less than unity
Equal to velocity ratio of a gear train
Always greater than unity
Reciprocal of velocity ratio of a gear train

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Theory of Machine
In a Hartnell governor, the stiffness of the spring is given by (where S1 and S2 = Spring forces exerted on the sleeve at max. and min. radii of rotation, and h = Compression of the spring)

(S₁ + S₂) / 2h
(S₁ - S₂) / 2h
(S₁ + S₂) / h
(S₁ - S₂) / h

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Theory of Machine
A Hartnell governor has its controlling force (Fc) given by Fc = ar + b, where r is the radius of rotation and a and b are constants. The governor becomes isochronous when

a is +ve and b = 0
a is +ve and b is also +ve
a is +ve and b is -ve
a = 0 and b is +ve

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Theory of Machine
In considering friction of a V-thread, the virtual coefficient of friction (μ₁) is given by

μ₁ = μ cos β
μ₁ = μ sin β
μ₁ = μ/cos β
μ₁ = μ/sin β

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