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Two objects, each with a mass of M, are positioned at a fixed distance of 2L apart. A smaller particle of mass m is launched from the midpoint of the line connecting their centers, moving in a direction perpendicular to this line. Given the gravitational constant G, which of the following statements is accurate?

1. The least velocity required for the particle of mass m to overcome the gravitational pull of the two objects is √(4GM / L)
2. The least velocity required for the particle of mass m to overcome the gravitational pull of the two objects is √(2GM / L)
3. The gravitational field strength due to the two objects is 2GM / L
4. The total energy of the particle of mass m remains unchanged

Correct answer: The least velocity required for the particle of mass m to overcome the gravitational pull of the two objects is √(4GM / L)

Solution

The least velocity required for the particle to escape the gravitational pull of the two objects is derived from energy conservation. The escape velocity is √(4GM / L), accounting for the combined gravitational potential of both masses.

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