An IIT-JEE 2007 Question on Centre of Mass

Here is an assertion-reason type MCQ (involving centre of mass motion) which appeared in IIT-JEE 2007 question paper:

STATEMENT-1

If there is no external torque on a body about its centre of mass, then the velocity of the centre of mass remains constant

because

STATEMENT-2

The linear momentum of an isolated system remains constant.

(a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct

explanation for Statement-1

(b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct

explanation for Statement-1

(c) Statement-1 is True, Statement-2 is False

(d) Statement-1 is False, Statement-2 is True

This is a very simple question meant for checking your understanding of basic principles. But if you are not careful, you are liable to pick out a wrong answer!

Generally, if there are external torques or forces or both, the velocity of the centre of mass will change. So, the condition of no external torque alone is not sufficient to ensure the constancy of the velocity of the centre of mass. Statement-1 is therefore false.

[You should also note that an external torque about the centre of mass will not change the velocity of the centre of mass].

Statement-2 is evidently true.

The correct option therefore is (d).