Question

The concept of centre of mass proves that laws of mechanics which are true for a point mass, are equally valid for all macroscopic bodies of any shape, size, mass, etc. For example, when vector sum of external forces acting on a system of particles is zero, the velocity of centre of mass of the system will remain constant.
Read the above passage and answer the following questions :
(i) Is centre of mass of a body a real point ?
(ii) Does centre of mass lie within the body always ?
(iii) How do you justify that `overset rarr(v_(cm)) =` constant ?

Answer 1

(i) No, centre of mass of a body is not a real point, as mass of body is distributed all over the body. It is never concentrated at the centre of mass. The concept of centre of mass is only theoretical, which helps us in simplifying the calculations.
(ii) No, not always, In certain cases, centre of mass of a body may be where there is no mass
(iii) When `overset rarr(F_(ext)) = sum overset rarr(F_(i)) = 0, m overset rarr(a_(cm)) = 0`
or `m.(d)/(dt) (overset rarr(v_(cm))) = 0 :. overset rarr(v_(cm)) =` constant