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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

cosecφ
cosφ
sinφ
secφ

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Theory of Machine
The velocity of a particle moving with simple harmonic motion, at any instant is given by (where ω = Displacement of the particle from mean position)

ω √(x² - r²)
ω² √(x² - r²)
ω √(r² - x²)
ω² √(r² - x²)

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Theory of Machine
If the radius of gyration of a compound pendulum about an axis through e.g. is more, then its frequency of oscillation will be

Less
More
Same
Data are insufficient to determine same

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Theory of Machine
A circle passing through the pitch point with its center at the center of cam axis is known as

Prime circle
Pitch circle
Outer circle
Base circle

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Theory of Machine
In a mechanism, usually one link is fixed. If the fixed link is changed in a kinematic chain, then relative motion of other links

Will remain same
Could change or remain unaltered depending on which link is fixed
Will change
Will not occur

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Theory of Machine
In a Hartnell governor, the lift of the sleeve is given by (where r₁ and r₂ = Max. and min. radii of rotation, x = Length of ball arm of the lever, and y = Length of sleeve arm of the lever)

(r₁ + r₂) (y/x)
(r₁ + r₂) (x/y)
(r₁ - r₂) (x/y)
(r₁ - r₂) (y/x)

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