Centre of mass of variable mass distribution in unique way explanation.

The centre of mass of a body

Centre of mass of a ring will be at a position:

Centre of mass of semi circular disc by two unique methods.

Calculate centre of mass of the system

Is centre of mass always a reality ?

Assertion: Centre of mass of a rigid body always lies inside the body. Reason: Centre of mass and centre of gravity coincide if gravity is uniform.

Consider a system of two particles having masses m_(1) and m_(2) . If the particle of mass m_(1) is pushed towards the centre of mass of particles through a distance d , by what distance would the particle of mass m_(2) move so as to keep the mass centre of particles at the original position?

Consider a sytem of two particles having masses m_(1) and m_(2) . If the particle of mass m_(1) is pushed towards the centre of mass of particles through a distance d , by what distance would the particle of mass m_(2) move so as to keep the mass centre of particles at the original position?

A random variable X has the following distribution

Find the centre of mass of the section. Consider the mass of the lamina to be uniformly distributed.