Three equal masses of \(m\) kg each are fixed at the vertices of an equilateral triangle \(ABC.\) What is the force acting on a mass \(2m\) placed at the centroid \(G\) of the triangle? 
(Take \(AG=BG=CG=1\) m.)

       

1. \(Gm^2(\hat{i}+\hat{j})\)
2. \(Gm^2(\hat{i}-\hat{j})\)
3. zero
4. \(2Gm^2(\hat{i}+\hat{j})\)

Three equal masses of \(m\) kg each are fixed at the vertices of an equilateral triangle \(ABC.\) What is the force acting on a mass \(2m\) placed at the centroid \(G\) of the triangle if the mass at the vertex \(A\) is doubled?
Take \(AG=BG=CG=1~\text{m}.\)

1.   \(Gm^{2}   \left(\hat{i} + \hat{j}\right)\)
2. \(Gm^{2}   \left(\hat{i} - \hat{j}\right)\)
3. \(0\)
4. \(2Gm^{2} \hat{j}\)$\stackrel{}{}$