A particle of mass ‘m’ is kept at rest at a height 3R from the surface of earth, where ‘R’ is radius of earth and ‘M’ is mass of earth. The minimum speed with which it should be projected, so that it does not return back, is (g is acceleration due to gravity on the surface of earth)

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(GM / R)^1/2. The minimum speed required for the particle to escape Earth's gravitational field is the escape velocity. At a height of 3R from the Earth's surface, the escape velocity is derived using the formula $ v = \sqrt{\frac{2GM}{r}} $, where $ r = 4R $ (distance from Earth's center). Substituting $ g = \frac{GM}{R^2} $, the escape velocity simplifies to $ \sqrt{\frac{GM}{R}} $.

A particle of mass ‘m’ is kept at rest at a height 3R from the surface of earth, where ‘R’ is radius of earth and ‘M’ is mass of earth. The minimum speed with which it should be projected, so that it does not return back, is (g is acceleration due to gravity on the surface of earth)

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