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Statement 1: If there is no external torque on the body about its centre of mass, then the velocity of the centre of mass remains constant.

Statement 2: The linear momentum of the isolated system remains constant.

(a) Statements 1 and 2 are true and statement 2 is the correct explanation of statement 1

(b) Statement one and two are true and statement2 is not the correct explanation of statement1

(c) Statement 1 is true, statement 2 is false

(d) Statement 2 is true, statement 1 is false

This question was addressed to me in exam.

This is a very interesting question from Moment of Inertia and its Significance in portion System of Particles and Rotational Motion of Engineering Physics I

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Correct choice is (d) Statement 2 is true, statement 1 is false

To elaborate: The absence of external torque does not ensure the absence of external force. If an external force is present, then the velocity of the centre of mass will not remain constant. Thus statement 1 is false.

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