i. The moment of the force F about the point
O is said to be positive when the tendency of rotation of the body takes place in the
anticlockwise direction, otherwise the moment is said to be negative.
ii. The S.I. unit of moment is Newton-metre (Nm). In C.G.S. system, the unit of momen
is dyne-centimetre.
iii. The algebraic sum of the moments of
2 or more forces about any point in their
plane is equal to the moment of their
resultant about the same point (Varignon's
theorem).
iv. A system of two equal and unlike parallel forces whose lines of action are not the
same is known as a couple or a torque. The
moment of a couple is the product of either
of the forces forming the couple and its
arm.Thus, moment of the couple
(F. p) = F. p.
V. The algebraic sum of the moments of
two forces forming a couple about any
point in their plane is constant.
vi. Two coplanar couples of equal and
opposite moments balance each other.
a. Three forces P, Q and R act along the sides AB, BC and BA respectively of an equilateral triangle ABC. Their resultant is parallel to BC and passes through the
centre of gravity G of triangle. Prove that
Q =R= P/2
b.If six forces of relative magnitudes 1, 2, 3, 4, 5 and 6 act on a rigid body along the sides of a regular hexagon, taken in order, show that the single equivalent force is of relative magnitude b and that it acts along a line parallel to the force 5 at a from the centre of the hexagon equal to 3 1/2 times the distance of a side from the centre.
please write answer part b only