- Center of Mass
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- Velocity of centre of mass
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- Acceleration of centre of mass
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- Kinetic energy of the system of particles
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- Linear Momentum of System of particles
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- Center Of Mass Frame of Reference
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- Center of Mass Problems with Solutions

- Included with Linear momentum
- Assignment 1
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- Assignment 2
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- Assignment 3
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- Assignment 4
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- Center of mass Problems for class 11

- Let there are n number of particles in a n particle system and these particles possess some motion. The motion of the i'th particle of this system would depend on the external force
**F**_{i}acting on it. Let at any time if the velocity of i'th particle be**v**_{i}then its kinetic energy would be

- Let
**r**_{i}be the position vector of the i'th particle w.r.t. O and**r'**_{i}be the position vector of the centre of mass w.r.t.**r**_{i},as shown below in the figure , then

**r**_{i}=**r'**_{i}+**R**_{cm}(2)

where**R**_{cm}is the position vector of centre of mass of the system w.r.t. O.

- Differentiating equation 2 we get

where**v**_{i}is the velocity of i'th particle w.r.t. centre of mass and**V**_{cm}is the velocity of centre of mass of system of particle. Putting equation 3 in 1 we get,

- Sum of Kinetic energy of all the particles can be obtained from equation 4

- Now last term in above equation which is

would vanish as it defines the null vector because

- Therefore kinetic energy of the system of particles is,

where,

is the kinetic energy obtained as if all the mass were concentrated at the centre of mass and

is the kinetic energy of the system of particle w.r.t. the centre of mass.

- Hence it is clear from equation 6 that kinetic energy of the system of particles consists of two parts: the kinetic energy obtained as if all the mass were concentrated at the centre of mass plus the kinetic energy of motion about the centre of mass.

- If there were no external force acting on the particle system then the velocity of the centre of mass of the system will remain constant and Kinetic Energy of the system would also remain constant.

Class 11 Maths Class 11 Physics Class 11 Chemistry

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