Physics · Acceleration due to gravity and its variation with altitude and depth
The height at which the value of acceleration due to gravity becomes of that at
The height at which the value of acceleration due to gravity becomes \( 50 \% \) of that at the surface of the earth. (radius of the earth \( =\mathbf{6 4 0 0 k m} \) ) is
- A. 2650
- B. 2430
- C. 2250
- D. 2350
Step-by-step solution
The acceleration due to gravity at height h is given by g' = g (R/(R+h))^2. Setting g' = 0.5 g gives (R/(R+h))^2 = 0.5, so R/(R+h) = 1/√2. Solving, h = R(√2 - 1). With R = 6400 km, h ≈ 6400 × 0.4142 ≈ 2650 km.
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