Theory of Machine
The two links OA and OB are connected by a pin joint at O. If the link OA turns with angular velocity ω₁ rad/s in the clockwise direction and the link OB turns with angular velocity ω₂ rad/s in the clockwise direction, then the rubbing velocity at the pin joint O is (where r = Radius of the pin at O)

(ω₁ - ω₂)2r
(ω₁ - ω₂)r
(ω₁ + ω₂)r
ω₁.ω₂.r

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Theory of Machine
Which of the following property of the instantaneous center is correct?

A rigid link rotates instantaneously relative to another link at the instantaneous centre for the configuration of the mechanism considered.
All of these
The velocity of the instantaneous centre relative to any third rigid link is same whether the instantaneous centre is regarded as a point on the first rigid link or on the second rigid link.
The two rigid links have no linear velocity relative to each other at the instantaneous centre.

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

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