Question

The acceleration due to gravity becomes \( \frac{g}{2} \) at a height equal to:

• A. \( \frac{R}{4} \)
• B. \( \frac{R}{2} \)
• C. \( \frac{R}{3} \)
• D. \( \frac{R}{5} \)

Hint:

For small heights, use approximation \(g_h \approx g(1 - 2h/R)\) instead of full formula.

Answer 1

The Correct Option is A

Concept: For small heights \(h \ll R\), \[ g_h \approx g\left(1 - \frac{2h}{R}\right) \]

Step 1: Apply condition \[ \frac{g}{2} = g\left(1 - \frac{2h}{R}\right) \]

Step 2: Simplify \[ \frac{1}{2} = 1 - \frac{2h}{R} \] \[ \frac{2h}{R} = \frac{1}{2} \] \[ h = \frac{R}{4} \] Conclusion \[ {h = \frac{R}{4}} \]