difference between center of mass and center of gravity?

Question

the equation to find the center of mass of a rigid object by giving examples.

Answer 1

Centre of mass- is the point in or outside a rigid body along which(not necessarily at which) when a force is applied on the body, than the body behaves like a point mass, i.e. the body moves along the direction of applied force, without any rotational motion.
Consider a system of particles of a rigid body and choose a point of reference in the space. Let m1, m2, m3,…….be the mass of the particles and r1, r2, r3…………be their position vectors respectively,
Then the position vector of the centre of mass will be
R= (m1r1+m2r2+………..mnrn )/ (m1+m2+…..+mn)
Centre of gravity- is the point at which the vector sum of the gravitational forces acting on all the particles of the rigid body acts, irrespective of the orientation of the rigid body. It can be found out by balancing the body on a pointer and equating the total clockwise moment and total anticlockwise moment acting on it.

Answer 2

The first answerer is absolutely correct. Thought I'd add, though:

When we talk about F = Ma, we are talking about a force (F) acting through the center of the mass (M) to give the mass an acceleration (a).

When that force is due to gravity, we write W = Mg; where weight (W) is the force acting through the center of mass (M) with the acceleration (g) due to gravity. In which case the center of mass is in fact the center of gravity.

Answer 3

Center of mass is the pt. where all the mass of the body maybe considered to be concentrated. center of gravity is the pt. where the gravitational force is applied(that is the point of application of gravitational force). The point of application of gravitational force is always at the centre of mass for a system, hence both are the same pt.s. However there are certain forces like buoyant force, which do not always act on the centre of mass. Buoyant force acts at the geometrical centre of the system, that is, it is the centre of mass of the system if mass were uniformly distributed everywhere in the system.