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Motion Of The Centre Of Mass MCQ - Practice Questions with Answers

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

Syllabus

Quick Facts

Motion of the centre of mass is considered one the most difficult concept.
19 Questions around this concept.

Solve by difficulty

EASY

Two identical particles move towards each other with velocity $2\nu$ and $\nu$ respectively. The velocity of the centre of mass is :

$\nu$

$\nu /3$

$\nu /2$

zero

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A body $A$ of mass M while falling vertically downwards under gravity breaks into two parts; a body B of mass $\frac{1}{3}M$ and another body $C$ of mass $\frac{2}{3}M$ . The center of mass of bodies B and $C$ taken together shifts compared to that of the body $A$ towards :

body $C$

body B

depends on height of breaking

does not shift

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Concepts Covered - 0

Motion of the centre of mass

Velocity of centre of mass

${\vec{v}_{CM}}=\frac{m_{1}\vec{v_{1}}+{m_{2}}\vec{v}_{2}........}{m_{1}+m_{2}........}$

m1, m2 ------- are mass of all the particles $\vec{v_{1}},\vec{v}_{2}......$ are velocities of all the particles.

Similarly momentum of the system = $P_{sys} = Mv_{cm}$

Acceleration of centre of mass

${\vec{a}_{CM}}=\frac{m_{1}\vec{a_{1}}+{m_{2}}\vec{a}_{2}........}{m_{1}+m_{2}........}$

m1, m2 are mass of all the particles $\vec{a_{1}}, \; \vec{a_{2}}....$ are their respective acceleration.

Similarly Net force on the system = $F_{net}= Mv_{cm}$

And $F_{net}= \vec{F_{ext}}\ +\ \vec{F_{int}}$

And we know that both action and reaction of an internal force must be within the system. In this way vector summation will cancel all internal forces and hence net internal force on the system is zero.

So $\vec{F_{net}} = M\vec{a_{cm}}$

If External Force = 0

$\vec{F}_{ext}=0\Rightarrow M\vec{a}_{cm}=0\Rightarrow \vec{a}_{cm}=0$

$if \ \vec{a}_{cm}=0 \Rightarrow v_{cm}=constant$

If $v_{cm}=constant \Rightarrow P_{sys}=constant$

So it implies that the total momentum of the system must remain constant.

i.e. if no external force is acting on the system, the net momentum of the system remains constant.This is nothing but the principle of conservation of momentum in absence of external forces.Which says ìIf resultant external force is zero on the system, then the net momentum of the system must remain constant.

Special case

If External Force = 0 and Velocity of Centre of Mass = 0

Then Then centre of mass remains at rest. Individual components of a system may move and have non zero momentum due to mutual forces but the net momentum of the system remains zero.