STATEMENT-1 If there is no external torque on | vedclass

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(D) The velocity of the center of mass $(v_{cm})$ is related to the total external force $(F_{ext})$ by the equation $F_{ext} = M a_{cm} = M (dv_{cm}/

Vedclass · Accepted Answer

Statement-$1$ is False,Statement-$2$ is True.

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(D) The velocity of the center of mass $(v_{cm})$ is related to the total external force $(F_{ext})$ by the equation $F_{ext} = M a_{cm} = M (dv_{cm}/dt)$.If the total external force is zero,then $a_{cm} = 0$,which implies $v_{cm}$ is constant.$STATEMENT-1$ states that there is no external torque. The absence of external torque implies that the angular momentum is conserved,but it does not necessarily imply that the total external force is zero.For example,a couple acting on a body produces torque but zero net force. Thus,$v_{cm}$ may change if there is a net force,even if there is no net torque.Therefore,$STATEMENT-1$ is False.$STATEMENT-2$ is a fundamental principle of mechanics (Law of Conservation of Linear Momentum) and is True.Thus,$STATEMENT-1$ is False and $STATEMENT-2$ is True.

$STATEMENT-1$ If there is no external torque on a body about its center of mass,then the velocity of the center of mass remains constant. because
$STATEMENT-2$ The linear momentum of an isolated system remains constant.

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$STATEMENT-1$ If there is no external torque on a body about its center of mass,then the velocity of the center of mass remains constant. because$STATEMENT-2$ The linear momentum of an isolated system remains constant.