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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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