Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation
Three equal masses m are positioned at the three vertices of an equilateral triangle of side a . Determine the force exerted by this system on another particle of mass m located at the mid-point of one of the sides.
Options
- A4Gm^2 3a^2
- BGm^2 3a^2
- C8Gm^2 3a^2
- D4Gm^2 a^2
Correct answer
A. 4Gm^2 3a^2
Step-by-step solution
Let the vertices of the equilateral triangle be A, B, and C, each having a mass m . Let the fourth mass m be placed at point D, which is the mid-point of the side BC. The distance of D from B and C is BD = CD = a 2 . The gravitational force exerted by the mass at B on the mass at D is F_B = Gm^2 ( a 2 )^2 = 4Gm^2 a^2 directed towards B. The gravitational force exerted by the mass at C on the mass at D is F_C = Gm^2 ( a 2 )^2 = 4Gm^2 a^2 directed towards C. Since F_B and F_C are equal in magnitude and opposite in di