Explanation:

The given problem involves the projectile motion of a body projected vertically upward with a certain velocity. We need to determine the height attained by the body.

Let's break down the problem into smaller steps to solve it systematically.

Step 1: Identify the given quantities:
- Initial velocity of the body: √(GM/R)
- Acceleration due to gravity: g = GM/R² (from the law of universal gravitation)
- Height attained by the body: ?

Step 2: Determine the time taken to reach the maximum height:
- When the body reaches the maximum height, its final velocity becomes zero (v = 0).
- Using the equation of motion, v = u + gt, where u is the initial velocity and g is the acceleration due to gravity, we can rewrite the equation as 0 = √(GM/R) - gt.
- Solving for t, we get t = √(GM/R) / g.

Step 3: Calculate the maximum height reached by the body:
- The equation for height in projectile motion is h = ut - 0.5gt².
- Substituting the values of u and t, we get h = (√(GM/R)) * (√(GM/R) / g) - 0.5g(√(GM/R) / g)².
- Simplifying this expression, h = (GM/R) - (GM/R).
- Therefore, the maximum height attained by the body is zero.

Step 4: Answer the question:
Since the maximum height attained by the body is zero, none of the given options (A) R/2, (B) R, (C) 5/4R, and (D) 3R/2 are correct.