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What is the position vector of centre of mass of the two particle system?

For two particle system, the position vector of centre of mass of the two particle system is given by,


$$\vec{r} = \frac {m_1 \vec{r_1} + m_2 \vec{r_2}}{m_1+m_2}$$



For two particle system, velocity of centre of mass is given by,


$$\vec{v_c} = \frac {m_1 \vec{v_1} + m_2 \vec{v_2}}{m_1+m_2}$$


Whewe,


\(m_1\) and \(m_2\) are the masses of two particles.


\(\vec{r_1}\) and \(\vec{r_2}\) are the position vector of the particles \(m_1\) and \(m_2\) respectively.


\(\vec{v_1}\) and \(\vec{v_2}\) are velocities of the particles \(m_1\) and \(m_2\) respectively.

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How many fundamental and supplementary units in SI?

In SI, there are seven base ( fundamental ) units and two supplementary units.
Base unit

Physical quantity


Unit


Symbol




Mass


Kilogram


kg




Length


Metre


m





Time


Second


s





Temperature


Kelvin


K





Electric current


Ampere


A





Luminous intensity


Candela


cd





Quantity of matter


Mole


mol




Supplementary units


Physical quantity


Unit


Symbol




Plane angle


Radian


rad





Solid angle


Steradian


sr



Conversion factor
Conversion of length

1 centimetre = 10-2 metre
1 millimetre = 10-3metre
1 micrometre = 10-6metre
1 nanometre = 10-9 metre
1 angstrom= 10-10 metre
1 fermi = 10-15 metre
1 kilometre = 103 metre
1 austronomical unit = 1AU=1.496 × 1011 metre
1 light year = 1 ly = 9.461 ×1015metre
1 mile = 1.609 ×103 metre
1 yard = 0.9144 metre
1 inch = 0.0254 metre


Conversion of time

1 mili second= 10-3 second
1 micro second = 10-6 second
1 neno second = 10-9 second
1 hour = 60 minute = 3600 second
1 day = 24 hours =86400 second
1 year = 365 day = 3.156× 107 second
1 sec = 10-8second


Conversion of mass

1 gram = 10 -3 kg
1 quintal = 100 kg
1 tonne = 1000 kg
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