## Theory of Machine The primary unbalanced force due to inertia of reciprocating parts in a reciprocating engine is given by (where m = Mass of reciprocating parts, ω = Angular speed of crank, r = Radius of crank, θ = Angle of inclination of crank with the line of stroke, and n = Ratio of the length of connecting rod to radius of crank)

m.ω².r sinθ
m.ω².r cosθ
m.ω².r (cos 2θ/n)
m.ω².r (sin 2θ/n)

15
8
30
28

## Theory of Machine The maximum efficiency of spiral gears is (where θ = Shaft angle, and φ = Friction angle)

sin (θ + φ) + 1/ cos (θ - φ) + 1
cos (θ - φ) + 1/ cos (θ + φ) + 1
cos (θ - φ) + 1/ sin (θ + φ) + 1
cos (θ + φ) + 1/ cos (θ - φ) + 1

## Theory of Machine The contact ratio is given by

(Length of the arc of contact)/(Circular pitch)
(Length of the path of approach)/(Circular pitch)
(Length of the arc of approach)/cosφ
(Length of path of recess)/(Circular pitch)

## Theory of Machine The example of higher pair is

All of these
Belt, rope and chain drives
Ball and roller bearings
Gears, cams

## Theory of Machine The engine of an aeroplane rotates in clockwise direction when seen from the tail end and the aeroplane takes a turn to the left. The effect of gyroscopic couple on the aeroplane will be

To raise the nose and dip the tail
To raise the nose and tail
To dip the nose and tail
To dip the nose and raise the tail