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

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Theory of Machine
Which of the following statement is correct for involute gears?

The interference is inherently absent.
The pressure angle is constant throughout the teeth engagement.
A convex flank is always in contact with concave flank.
The variation in centre distance of shafts increases radial force.

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Theory of Machine
In a steam engine, one method of obtaining the earlier cut-off with a simple slide valve is by increasing the angle of advance of the eccentric while the throw of the eccentric, steam lap and exhaust lap are kept constant. This method will

Reduce length of effective stroke of piston
Cause withdrawing or throttling of steam
All of these
Reduce maximum opening of port to steam

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