Statement -1- If there is no external torque on a body about...

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. Statement $-2-$ The Linear momentum of an isolated system remains constant. $\{\mathrm{A}\}$ Statement $-1$ is correct (true), Statement $-2$ is true and Statement- 2 is correct explanation for Statement - 1 $\{B\}$ Statement $-1$ is true, statement $-2$ is true but statement $-2$ is not the correct explanation four statement $-1$. $\{\mathrm{C}\}$ Statement $-1$ is true, statement- 2 is false \{D $\}$ Statement- 2 is false, statement $-2$ is true

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. Statement $-2-$ The Linear momentum of an isolated system remains constant.
$\{\mathrm{A}\}$ Statement $-1$ is correct (true), Statement $-2$ is true and Statement- 2 is correct explanation for Statement - 1
$\{B\}$ Statement $-1$ is true, statement $-2$ is true but statement $-2$ is not the correct explanation four statement $-1$.
$\{\mathrm{C}\}$ Statement $-1$ is true, statement- 2 is false
\{D $\}$ Statement- 2 is false, statement $-2$ is true

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Key Concepts

External Torque and Angular Momentum

External torque is responsible for changing the angular momentum of a system about a chosen point, often the center of mass. This concept underscores that the conditions for rotational dynamics (no external torque leading to conservation of angular momentum) are independent of the conditions required for translational (center-of-mass) motion, which relies on net external forces.

Center of Mass Dynamics

This concept concerns the motion of the center of mass of a body and is governed by Newton’s second law for translation (F_net = m * a). The key point is that for the velocity of the center of mass to remain constant, there must be no net external force acting on the body. The absence of an external torque does not guarantee that no net force is present, and hence it does not by itself ensure constant translational velocity.

Linear Momentum Conservation

This principle states that in an isolated system, where no net external force acts, the total linear momentum remains constant. It is a cornerstone of mechanics and is crucial in understanding that conservation of linear momentum is linked to the absence of net external forces, not the absence of external torques.

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