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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 essential condition of placing the two masses, so that the system becomes dynamically equivalent, is (where l₁ and l₂ = Distance of two masses from the centre of gravity of the body, and kG = Radius of gyration of the body)

l₂ = kG
l₁l₂ = kG
l₁ = kG
l₁l₂ = kG²

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Theory of Machine
One end of a helical spring is fixed while the other end carries the load W which moves with simple harmonic motion. The frequency of motion is given by (where δ = Deflection of the spring)

1/2π. √(g/δ)
2π. √(g/δ)
1/2π. √(δ/g)
2π. √(δ/g)

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Theory of Machine
The power of a Porter governor is equal to

[4c²/(1 + 2c)] (m + M) g.h
[3c²/(1 + 2c)] (m + M) g.h
[c²/(1 + 2c)] (m + M) g.h
[2c²/(1 + 2c)] (m + M) g.h

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Theory of Machine
In automobiles the power is transmitted from gear box to differential through

Universal joint
Hooke's joint
Knuckle joint
Bevel gear

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Theory of Machine
The rotor of a ship rotates in clockwise direction when viewed from stern and the ship takes a left turn. The effect of gyroscopic couple acting on it will be

To raise the stern and lower the bow
To raise the bow and stern
To lower the bow and stern
To raise the bow and lower the stern

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