Assertion : If no external force acts on a sy | vedclass

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Question

(C) The acceleration of the centre of mass is given by $F_{	ext{ext}} = M a_{CM}$. If the net external force $F_{	ext{ext}} = 0$,then $a_{CM} = 0$.

Vedclass · Accepted Answer

If the $Assertion$ is correct but $Reason$ is incorrect.

Vedclass · Answer

(C) The acceleration of the centre of mass is given by $F_{	ext{ext}} = M a_{CM}$. If the net external force $F_{	ext{ext}} = 0$,then $a_{CM} = 0$. This implies that the velocity of the centre of mass $v_{CM}$ remains constant. If the system is initially at rest,it will remain at rest. If it is moving,it will continue to move with a constant velocity. Thus,the statement that the centre of mass will not move in any direction is only true if the initial velocity is zero. However,generally,the centre of mass continues its state of motion. The $Reason$ states that if the net external force is zero,the linear momentum changes. This is incorrect because,according to Newton's second law,$\frac{dP}{dt} = F_{	ext{ext}}$. If $F_{	ext{ext}} = 0$,then $\frac{dP}{dt} = 0$,which means the linear momentum $P$ is conserved (constant),not changing. Therefore,the $Assertion$ is partially correct (in the context of a stationary system) but the $Reason$ is clearly incorrect.

$Assertion$ : If no external force acts on a system of particles,then the centre of mass will not move in any direction.
$Reason$ : If net external force is zero,then the linear momentum of the system changes.

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$Assertion$ : If no external force acts on a system of particles,then the centre of mass will not move in any direction. $Reason$ : If net external force is zero,then the linear momentum of the system changes.