• Engineering and Architecture
  • Management and Business Administration
  • Medicine and Allied Sciences
  • Law
  • Animation and Design
  • Media, Mass Communication and Journalism
  • Finance & Accounts
  • Computer Application and IT
  • Pharmacy
  • Hospitality and Tourism
  • Competition
  • School
  • Study Abroad
  • Arts, Commerce & Sciences
  • Learn
  • Online Courses and Certifications
  1. Home
  3. Study Material
  4. Motion Of The Centre Of Mass - Practice Questions & MCQ

Motion Of The Centre Of Mass - Practice Questions & MCQ

Updated on Sep 18, 2023 18:34 AM

Quick Facts

  • Motion of the centre of mass is considered one the most difficult concept.

  • 11 Questions around this concept.

Solve by difficulty

QuestionEASY

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

View Solution

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 :

View Solution

Concepts Covered - 1

Motion of the centre of mass

  1. Velocity of the 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}

  1. 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}= Ma_{cm}

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

And we know that both the 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}}

 

  1. 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 ìf 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 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.

Study it with Videos

Motion of the centre of mass

Study other Related Concepts

Motion Of The Centre Of Mass Current Topic

Rotational Motion Of Rigid Body
Center Of Mass
Center Of Mass Of The Uniform Rod
Centre Of Mass Of Semicircular Ring
Centre Of Mass Of Semicircular Disc
Centre Of Mass Of A Triangle
Centre Of Mass Of Hollow Hemisphere
Centre Of Mass Of Solid Hemisphere
Centre Of Mass Of Hollow Cone
Centre Of Mass Of A Solid Cone

"Stay in the loop. Receive exam news, study resources, and expert advice!"

Get Answer to all your questions

Download Careers360 App
All this at the convenience of your phone

  • Regular Exam Updates

  • Best College Recommendations

  • College & Rank predictors

  • Detailed Books and Sample Papers

  • Question and Answers

Scan and download the app

OR

Explore Top Colleges Accepting Applications
Back to top