What's moment of weight? I have googled this out but no where found my answer .
My book states that the Centre Of Gravity of a body is the point about which the sum of moment of weights of all particles constituting the body is zero. No reasonable explanation is given here of the mentioned term. 
Could someone please help me with this and also explain why is it used in the definition?
 A: The $n^{\mathrm{th}}$ moment of some distribution, $f(x)$, is defined as: $$\int x^n f(x) \operatorname{d}x,$$ where it is understood that the integration is over all values of $x$. So, if you take the first moment and divide by the zeroth moment when $f$ is the mass density you get the center of mass. In probability theory, when $f$ is the probability density function, this is also known as the mean value of $x$. You can show, by combining the definition with some algebra, that if the center of mass is at $x=0$ then the first moment in that coordinate system will vanish.
Other applications where this is used:


*

*The moment of inertia is the traceless part of the matrix of second moments of the mass density.

*The multipole moments used for calculating electric, magnetic, and gravitational fields are tensor moments of charge, current, and mass densities, respectively.

A: In simple language you can say that There are infinitely many points in a rigid body and each point have a small mass,now this small mass give a torque to body."The centre of gravity is such a point about which Moments of weight is zero" means that about centre of gravity there is always a particle which produce a torque opposite to another particle and thus the body remain in rotational equilibrium(because no torque is acting on it).You must have heard people saying that you can balance every body in this world on its its centre of gravity,the reason is same which i given you.
A: A moment of a force, is the torque produced by that force acting at a distance. If the force magnitude is $W$ and the minimum distance of the line of action $h$ then the moment of the force is $\tau = h\, W$
The center of gravity is the point where $$\sum_{i~=~1}^n h_i W_i = 0$$
Considering only horizontal distances $r_i$ of each vertical force $W_i$ the above is
$$ \sum_{i~=~1}^n (r_i-c) W_i = 0 $$
and it is solved for $c$ to find the center of mass
$$ c = \frac{ \displaystyle\sum_{i~=~1}^n r_i\, W_i }{ \displaystyle\sum_{i~=~1}^n W_i }\,. $$
