Theory of Machine
A shaft has two heavy rotors mounted on it. The transverse natural frequencies, considering each of the rotor separately, are 100 Hz and 200 Hz respectively. The lowest critical speed is

6,000 r.p.m.
12,000 r.p.m.
9,360 r.p.m.
5,367 r.p.m.

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Theory of Machine
Two pulleys of radii r₁ and r₂ and at distance x apart are connected by means of an open belt drive. The length of the belt is

π (r₁ - r₂) + (r₁ + r₂)²/x + 2x
π (r₁ + r₂) + (r₁ - r₂)²/x + 2x
π (r₁ - r₂) + (r₁ - r₂)²/x + 2x
π (r₁ + r₂) + (r₁ + r₂)²/x + 2x

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Theory of Machine
The frictional torque transmitted in a flat collar bearing, considering uniform wear, is (where r₁ and r₂ = External and internal radii of collar respectively)

(2/3) μ W (r₁ + r₂)
(2/3) μ W [(r₁³ - r₂³)/(r₁² - r₂²)]
(1/2) μ W [(r₁³ - r₂³)/(r₁² - r₂²)]
(1/2) μ W (r₁ + r₂)

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Theory of Machine
For dynamic balancing of a shaft

None of these
The net dynamic force acting on the shaft is equal to zero
Both (A) and (B)
The net couple due to the dynamic forces acting on the shaft is equal to zero

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