Question

there are two massedM and 2M located at (1,-1) and (-2,4) then centre of mass system​

Answer 1

Two point masses m and 2m are lying at the points (1,-1) and (-2,4).

We have to find the location of the centre of mass.

Coordinates of the COM are given as :

$\sf X_{COM} = \dfrac{m_1x_1 + m_2x_2}{m_1 + m_2}$

$\sf Y_{COM} = \dfrac{m_1y_1 + m_2y_2}{m_1 + m_2}$

Now,

$\sf X_{COM} = \dfrac{1 \times m - 2 \times 2m}{m + 2m} \\ \\ \longrightarrow \sf X_{COM} = \dfrac{m - 4 m}{3m} \\ \\ \longrightarrow \sf X_{COM} = - \dfrac{3 m}{3m} \\ \\ \longrightarrow \boxed{ \boxed{ \sf X_{COM} = - 1}}$

Similarly,

$\sf Y_{COM}= \dfrac{ - 1 \times m + 4\times 2m}{m + 2m} \\ \\ \longrightarrow \sf Y_{COM} = \dfrac{ - m + 8 m}{3m} \\ \\ \longrightarrow \sf Y_{COM} = \dfrac{7 m}{3m} \\ \\ \longrightarrow \boxed{ \boxed{ \sf Y_{COM} = \dfrac{7}{3} }}$

The coordinates of the COM are (-1,7/3).