Q.Select WRONG statement about centre of mass: (A) Centre of mass of a 'C' shaped uniform rod can never be a point on that rod. (B) If the line of action of a force passes through the centre of mass, the moment of that force is zero. (C) Centre of mass of our Earth is not at its geometrical centre. (D) While balancing an object on a pivot, the line of action of the gravitational force of the earth passes through the centre of mass of the object.

[!TLDR] The WRONG statement is (A) -- the centre of mass of a 'C' shaped rod actually lies in the empty gap of the C, not on the rod material itself, but that does not make statement (A) correct; checking each option shows (A) is the …

Statement (B) is TRUE: if a force's line of action passes through the centre of mass, its position vector r (from the c.m.) is zero or parallel to itself, so the moment $\vec{r}\times\vec{F}$ about the c.m. is indeed zero. Statement (C) is TRUE: the Earth's mass distribution is not perfectly uniform/symmetric (internal density variations, tectonic mass distribution etc.), so its true centre of mass is not exactly at its geometric centre, though very close to it. Statement (D) is TRUE: this is precisely the plumb-line-suspension principle used to define/locate the centre of gravity/mass, i.e. the definition of balancing on a pivot. Statement (A) claims the c.m. of a C-shaped rod can NEVER lie on the rod material -- but this is stated as an absolute impossibility, which is not correct as a bl …

Check each of the four statements against the definitions and properties of centre of mass from 4.13.4 and elimi …

Assuming the c.m. of any 'hollow' or open shape must always fall in empty space away from the material -- while often true, treating it as an absol …