Question

Three equal masses M are placed at the vertices A, B, and C of an equilateral triangle. The net force acting on a unit mass placed at the centroid O is:

• A. Zero
• B. $3GM^{2}/L^{2}$
• C. $GM/L^{2}$
• D. $2GM/L^{2}$

Hint:

The center of symmetry for identical masses always has zero net field.

Answer 1

The Correct Option is A

Step 1: Concept
The net force is the vector sum of gravitational intensities from each mass.
Step 2: Analysis
At the centroid of an equilateral triangle with equal masses at the vertices, the forces $\vec{F}_{1}, \vec{F}_{2}, \vec{F}_{3}$ are equal in magnitude and separated by $120^{\circ}$.
Step 3: Conclusion
The vector sum $\vec{F}_{1} + \vec{F}_{2} + \vec{F}_{3} = 0$ because the resultant of any two is equal and opposite to the third.
Final Answer: (A)