The tractive force in a locomotive with two cylinders is given by (where c = Fraction of reciprocating parts per cylinder, m = Mass of reciprocating parts, ω = Angular speed of crank, r = Radius of crank, and θ = Angle of inclination of crank to the line of stroke)

m.ω2.r cos θ
c.m.ω2.r sin θ
(1 – c)m.ω2.r(cos θ – sin θ)
m.ω2.r(cos θ – sin θ)
✅ The correct answer is option C.

In order to give the primary balance of the reciprocating parts of a multi-cylinder in-line engines,

the algebraic sum of the primary forces must be equal to zero
the algebraic sum of the couples about any point in the plane of the primary forces must be equal to zero
both (a) and (b)
none of these
✅ The correct answer is option C.

A disturbing mass m1 attached to the rotating shaft may be balanced by a single mass m2 attached in the same plane of rotation as that of m1, such that (where r1 and r2 are the radii of rotation of m1 and m2 respectively)

m1r2 = m2r1
m1r1 = m2r2
m1m2 = r1r2
none of these
✅ The correct answer is option B.