Physics · GRAVITATION

Three equal masses of mass \( m \) are fixed at the vertices of an equilateral triangle \( ABC \) with distances from centroid \( G \) being \( AG = BG = CG = 1\text{ m} \). If the mass at vertex \( A \) is doubled to \( 2m \), what is the magnitude of the net gravitational force on a mass of \( 2m \) kept at centroid \( G \)?

1. A
   \( 4Gm^2 \)
2. B
   \( 8Gm^2 \)
3. C
   \( Gm^2 \)
4. D
   \( 2Gm^2 \)