Theory of Machine
The tractive force in a locomotive with two cylinders is given by (where c = Fraction of reciprocating parts per cylinder, m = Mass of reciprocating parts, ω = Angular speed of crank, r = Radius of crank, and θ = Angle of inclination of crank to the line of stroke)

m.ω².r (cosθ - sinθ)
m.ω².r cosθ
(1 - c).m.ω².r (cosθ - sinθ)
m.ω².r sinθ

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Theory of Machine
The frictional torque transmitted in a flat collar bearing, considering uniform pressure, is (where r₁ and r₂ = External and internal radii of collar respectively)

(2/3). μ W [(r₁³ - r₂³)/(r₁² - r₂²)]
(1/2). μ W (r₁ + r₂)
(1/2). μ W [(r₁³ - r₂³)/(r₁² - r₂²)]
(2/3). μ W (r₁ + r₂)

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Theory of Machine
Higher pairs are those which have

Two elements that permit relative motion
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

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Theory of Machine
When a mass of a critically damped single degree of freedom system is deflected from its equilibrium position and released, then it will

Oscillate with increasing time period
Return to equilibrium position without oscillation
Oscillate with constant amplitude
Oscillate with decreasing amplitude

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