91影视

Centre of massis the point on a structure which characterizes the motion of the object if the whole mass of that object is concentrated on that point.

${\mathrm{m}}_1{\stackrel{藱}{\mathrm{v}}}_1={\mathrm{F}}_{2\mathrm{on}1}$ _鈥�..(1)

And

${\mathrm{m}}_2{\stackrel{藱}{\mathrm{v}}}_2={\mathrm{F}}_{1\mathrm{on}2}$ 鈥�.. (2)

As you know,

$-{\mathrm{F}}_{2\mathrm{on}1}={\mathrm{F}}_{1\mathrm{on}2}$ 鈥�.. (3)

Hence, by adding equations (1) and (2) and then using (3), you get,

$m_1\stackrel{\boxed{?}}{v_1}+m_2\stackrel{\boxed{?}}{v_2}=0$ 鈥�.. (4)

If you divide eq. (4) by ${\mathrm{m}}_1+{\mathrm{m}}_2$, you get,

${\stackrel{藱}{\mathrm{v}}}_{\mathrm{cm}}=0$or ${\stackrel{藱}{\mathrm{v}}}_{\mathrm{cm}}=\mathrm{constant}$

Relative motion of an object is its motion with respect to any other moving or stationary object.

${\stackrel{\mathbf{藱}}{\mathbf{v}}}_{\mathbf{rel}}\mathbf{=}\stackrel{\mathbf{藱}}{{\mathbf{v}}_{\mathbf{2}}}\mathbf{-}{\stackrel{\mathbf{藱}}{\mathbf{v}}}_{\mathbf{1}}$

If you rearrange and subtract equation (1) from equation (2), you get,

$$\begin{gathered} {\stackrel{藱}{v}}_2=-{\stackrel{藱}{v}}_1=\frac{F_{1on2}}{m_2}-\frac{F_{2on1}}{m_1} \\ =\left(\frac{1}{m_2}+\frac{1}{m_1}\right)F_{1on2} \\ {\stackrel{藱}{v}}_{rel}=\frac{\left(m_1+m_2\right)}{m_1{m}_2}{F}_{Mutual} \\ =\left(\frac{1}{渭}\right)F_{Mutual} \end{gathered}$$

Where, $\mathrm{渭}=\frac{{\mathrm{m}}_1{\mathrm{m}}_2}{\left({\mathrm{m}}_1+{\mathrm{m}}_2\right)}$