Theory of Machine
Torsional vibrations are said to occur when the particles of a body moves

In a circle about its axis
Parallel to its axis
Perpendicular to its axis
None of these

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Theory of Machine
In the below figure, PC is the connecting rod and OC is the crank making an angle θ with the line of stroke PO and rotates with uniform angular velocity at ω rad/s. The Klien's acceleration diagram for determining the acceleration of the piston P is shown by quadrilateral CQNO, the acceleration of the piston is _________ when the crank OC and connecting rod PC are at right angles to each other.

Zero
Any +ve value
Infinity
Any -ve value

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Theory of Machine
The static balancing is satisfactory for low speed rotors but with increasing speeds, dynamic balancing becomes necessary. This is because, the

Unbalanced forces are not dangerous at higher speeds
Unbalanced couples are caused only at higher speeds
Effects of unbalances are directly proportional to the speed
Effects of unbalances are proportional to the square of the speed

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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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