Question

Assertion :If there is no external torque acting on a body about its center of mass, then the velocity of the center of mass remains constant. Reason: The linear momentum of an isolated system remains constant.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is incorrect but Reason is correct
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is C Assertion is incorrect but Reason is correct

For an isolated system: $F_{external}=0$

Now $\frac{dP}{dt}=F_{external}=0⟹P=constant$

Hence linear momentum of an isolated system is conserved.

Statement 1 is false. Lets take an example, consider an external force acting on the centre of mass of a body placed on a smooth surface.

Net torque about point O is zero but there is net force acting on the body.

$ma=F⟹a=\frac{F}{m}$

Thus velocity of COM will continously change because of the acceleration $a.$