An object is initially at rest at a height 3R above the Earth's surface, where R is Earth's radius. The minimum speed with which it must be projected so that it does not return to Earth is:
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Question

An object is initially at rest at a height 3R above the Earth's surface, where R is Earth's radius. The minimum speed with which it must be projected so that it does not return to Earth is:

G1 Physics · Accepted Answer

The object is at height 3R above the surface, so its distance from Earth's centre is r = R+3R = 4R. Escape speed from distance r is v e v_e v e ​ = √(2GM/r). Therefore, v e v_e v e ​ = √[2GM/(4R)] = √(GM/(2R)). Correct option: A.