Assertion: The position of centre of mass relative to body is independ...
Explanation:
The position of the centre of mass is defined as the point where the entire mass of the body can be assumed to be concentrated. The position of the centre of mass is independent of the choice of the coordinate system. This means that the position of the centre of mass of a body will remain the same irrespective of the coordinate system used to describe it.
Proof:
Let us assume that a body with mass M is composed of N particles, each with a mass mi and position vector ri. The position vector of the centre of mass of the body is given by:
R = (m1r1 + m2r2 + … + mN rN) / M
This equation shows that the position of the centre of mass is a function of the positions and masses of all the particles in the body.
If we change the coordinate system, the position vectors of the particles will change, but their masses will remain the same. This means that the position vector of the centre of mass will also change, but its value will remain the same.
Explanation of the Reason:
The reason why the position of the centre of mass is independent of the choice of the coordinate system is that the centre of mass does not shift its position in the absence of external forces. This is known as the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum of a system remains constant unless acted upon by an external force. If there is no external force acting on a body, the momentum of the body will be constant. This means that the velocity of the centre of mass will also be constant.
Since the velocity of the centre of mass is constant, its position will not change. This means that the position of the centre of mass will remain the same irrespective of the choice of the coordinate system used to describe it.
Assertion: The position of centre of mass relative to body is independ...
I think assertion is incorrect but reason is correct.