Question

two bodies of masses m1 and m2 are at distance x1 and x2 from their centre of mass then the

Answer 1

Explanation:

Given :  two bodies of masses m₁ and m₂ are at distance x₁ and x₂ from their center of mass

To Find :  the relation between m₁ , m₂  , x₁ and x₂

Solution:

two bodies of masses m₁ and m₂ are at distance x₁ and x₂ from their center of mass

Then  m₁x₁  + m₂x₂ = 0

m₁x₁  + m₂x₂ = 0

to Understand this lets call center of Mass as Origin

Then  m₁ and m₂ are at distance x₁ and x₂ from Origin

Then Center of Mass  =   (m₁x₁  + m₂x₂)/(m₁   + m₂)

Center of Mass  is assumed at Origin

=> (m₁x₁  + m₂x₂)/(m₁   + m₂) = 0  

=> m₁x₁  + m₂x₂ = 0

Answer 2

Given:

Two bodies of masses m1 and m2 are at distance x1 and x2 .

To find:

Coordinate of the centre of mass ?

Calculation:

Let the coordinates of the masses be :

• m1 : (x1,0)
• m2 : (x2,0)

Now, the X coordinate of Centre of Mass:

$\therefore \: \bar{x} = \dfrac{ \sum( m_{i} x_{i}) }{ \sum( m_{i}) }$

$\implies \: \bar{x} = \dfrac{ ( m1)(x1) + (m2)(x2) }{ (m1) + (m2) }$

Now, the Y coordinate of Centre of Mass:

$\therefore \: \bar{y} = \dfrac{ \sum( m_{i} y_{i}) }{ \sum( m_{i}) }$

$\implies \: \bar{y} = \dfrac{ ( m1)(0) + (m2)(0) }{ (m1) + (m2) }$

$\implies \: \bar{y} = 0$

So, net coordinate:

$\: (\bar{x}, \bar{y}) = \bigg[\dfrac{ ( m1)(x1) + (m2)(x2) }{ (m1) + (m2) } ,0 \bigg]$