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    Question

    An object is projected vertically upward from Earth's

    surface with speed  v 0 = √(GM/1.5R). The maximum height reached from the center of Earth is:
    A 1.5R Correct Answer Incorrect Answer
    B 3R Correct Answer Incorrect Answer
    C 5R Correct Answer Incorrect Answer
    D R Correct Answer Incorrect Answer

    Solution

    We are given:

    • Initial speed: v0 = √(GM/1.5R)
    • Object is projected vertically upward from Earth’s surface (i.e., from distance   r = R)
    • We are to find the maximum height from Earth’s center , denoted as rmax
    We'll apply conservation of mechanical energy between the point of projection and the highest point. Kinetic energy at launch: At the highest point, speed becomes zero, so only potential energy exists. Let the distance from Earth's center at maximum height be rmax Then:

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