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Theory of Machine

Theory of Machine
For an involute gear, the ratio of base circle radius and pitch circle radius is equal to

secφ
cosφ
cosecφ
sinφ

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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 anticlockwise 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
A torsional system with discs of moment of inertia I₁ and I₂ as shown in the below figure, is gear driven such that the ratio of speed of shaft B to shaft A is 'G'. Neglecting the inertia of gears, the equivalent inertia of disc on shaft B at the speed of shaft A is equal to

G².I₂
I₂/G
G.I₂
I₂/G²

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Theory of Machine
A mass of 1 kg is attached to the end of a spring with a stiffness of 0.7 N/mm. The critical damping coefficient of this system is

52.92 N-s/m
529.2 N-s/m
1.4 N-s/m
18.52 N-s/m

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Theory of Machine
A Hartnell governor has its controlling force (Fc) given by Fc = ar + b, where r is the radius of rotation and a and b are constants. The governor becomes isochronous when

a is +ve and b = 0
a is +ve and b is also +ve
a = 0 and b is +ve
a is +ve and b is -ve

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Theory of Machine
The tendency of a body to resist change from rest or motion is known as

Inertia
Mass
Friction
Resisting force

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