Physics · GRAVITATION

Three particles of mass \( m \) each are situated at the vertices \( A, B, C \) of an equilateral triangle, with centroid at \( G \), as shown in the diagram. If a particle of mass \( 2m \) is placed at centroid \( G \), what is the resultant gravitational force on this mass at \( G \)?

1. \( 0 \)
2. \( \frac{2Gm^2}{r^2} \hat{\mathbf{j}} \)
3. \( \frac{4Gm^2}{r^2} \hat{\mathbf{j}} \)
4. \( \frac{6Gm^2}{r^2} \hat{\mathbf{i}} \)