Theory of Machine
The partial balancing of reciprocating parts in locomotives produces

Swaying couple
Variation in tractive force along the line of stroke
Hammer blow
All of these

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Theory of Machine
The secondary unbalanced force due to inertia of reciprocating parts in a reciprocating engine is given by (where m = Mass of reciprocating parts, ω = Angular speed of crank, r = Radius of crank, θ = Angle of inclination of crank with the line of stroke, and n = Ratio of the length of connecting rod to radius of crank)

m.ω².r (sin 2θ/n)
m.ω².r cosθ
m.ω².r sinθ
m.ω².r (cos 2θ/n)

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

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Theory of Machine
For dynamic balancing of a shaft

None of these
The net dynamic force acting on the shaft is equal to zero
Both (A) and (B)
The net couple due to the dynamic forces acting on the shaft is equal to zero

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