- Three particles of masses \(4 m , 2 m\) and \(k m\) are placed at the points with coordinates \(( - 3 , - 1 ) , ( 6,1 )\) and \(( - 1,5 )\) respectively.
Given that the centre of mass of the three particles is at the point with coordinates \(( \bar { x } , \bar { y } )\)
- show that \(\bar { x } = \frac { - k } { k + 6 }\)
- find \(\bar { y }\) in terms of \(k\).
Given that the centre of mass of the three particles lies on the line with equation \(y = 2 x + 3\)
- find the value of \(k\).
A fourth particle is placed at the point with coordinates \(( \lambda , 4 )\).
Given that the centre of mass of the four particles also lies on the line with equation \(y = 2 x + 3\) - find the value of \(\lambda\).