Question

What is the position of centre of mass from two bodies. Take them as r1 , r2 and find them .
If m1 = m2 what about CM & d
If m1 < m2 , What about CM & d

Answer 1

The distance of centre of mass is inversely proportional to mass of particle.

Let the masses be m1 , m2 and Let the distance of centre of mass from first & second body respectively is r1 , r2 .
The distance of separation of the masses is d ( = r1 + r2)
r ∝ 1/m

r1 /r2 = m2/m1

Adding 1 on both sides,
(r1 + r2)/r2 = (m2+m1)/m1

d/r2 = m2 + m1 / m1

r2 = m1 ( d ) / m1 + m2

Also,

r2/r1 = m1/m2

Add 1 on both sides

(r2 + r1) / r1 =( m1 + m2 )/ m2

d/r1 = (m1 + m2)/m2

r1 = m2 ( d) / m1 + m2 .


If m1 = m2 , then r1 = r2= d/2 ,
The centre of mass will lie along the mid points of the line joining them .

If m1 < m2 , then centre of mass lies near to m2 and r2 < r1 .