Theory of Machine
The instantaneous center of a rigid thin disc rolling on a plane rigid surface is located at

An infinite distance on the plane surface
The center of the disc
The point on the circumference situated vertically opposite to the contact point
The point of contact

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

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