Question

All the particles of a body are situated at a distance $R$ from the origin. The distance of the centre of mass of the body from the origin is

• A. $=R$
• B. $\le R$
• C. $>R$
• D. $\ge R$

Answer 1

The correct option is B $\le R$

(i) When all the particles are uniformly distributed.

If particles are uniformly distributed at distance $R$ from the origin then by symmetry, centre of mass will lie at origin. Therefore, distance of c.o.m of the body from origin will be zero.
(ii) When all the particles lie at same point at distance $R$ from the origin.

In this case, the c.o.m will lie at the same point itself at distance of $R$ from the origin. Therefore distance of c.o.m of the body from origin is $R$
iii)Non - uniform distribution lies between above two situations. In this case, c.o.m wil lie at distance less than $R$ as c.o.m will shift to more towards dense region from origin.

Therefore, distance of c.o.m of the body from origin is always $\le R$.