Theory of Machine
There are six gears A, B, C, D, E and F in a compound train. The numbers of teeth in the gears are 20, 60, 30, 80, 25 and 75 respectively. The ratio of angular speeds of the driven (F) to the driver (A) of the drive is

4/15
12
1/24
1/8

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Theory of Machine
Two heavy rotating masses are connected by shafts of lengths l₁, l₂ and l₃ and the corresponding diameters are d₁, d₂ and d₃. This system is reduced to a torsionally equivalent system having uniform diameter d = d₁ of the shaft. The equivalent length of the shaft is

l = l₁ + l₂.(d₁/d₂)³ + l₂.(d₁/d₃)³
l = l₁ + l₂.(d₁/d₂)⁴ + l₃.(d₁/d₃)⁴
l₁ + l₂ + l₃
(l₁ + l₂ + l₃)/3

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