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Two objects, each with mass M, are placed at a fixed distance of 2L apart. A particle of mass m is launched from the midpoint between these two objects in a direction perpendicular to the line connecting them. Given the gravitational constant G, which of the following statements is accurate?

1. The least initial speed required for the particle of mass m to escape the gravitational influence of the two objects is 4√(GM/L)
2. The least initial speed required for the particle of mass m to escape the gravitational influence of the two objects is 2√(GM/L)
3. The least initial speed required for the particle of mass m to escape the gravitational influence of the two objects is √(2GM/L)
4. The total energy of the particle of mass m remains unchanged

Correct answer: The least initial speed required for the particle of mass m to escape the gravitational influence of the two objects is 2√(GM/L)

Solution

The gravitational potential energy at the midpoint is used to calculate the escape velocity. The least initial speed required for the particle to escape is derived as 2√(GM/L) using energy conservation principles.

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