Question

At what height h above earth, the value of g becomes g/2? (R = Radius of earth)

• A. 3R
• B. $\sqrt{2}R$
• C. $(\sqrt{2}-1)R$
• D. $\frac{1}{\sqrt{2}}R$

Hint:

At what height h above earth, the value of g becomes g/2? (R = Radius of earth)

Answer 1

The Correct Option is C

Step 1: Concept
The acceleration due to gravity at height $h$ is given by: $$g' = g\frac{R^2}{(R+h)^2}$$
Step 2: Analysis
We are given $g' = g/2$. $$\frac{g}{2} = g\frac{R^2}{(R+h)^2} \Rightarrow \frac{1}{2} = \frac{R^2}{(R+h)^2}$$
Step 3: Calculation
Taking the square root: $\frac{1}{\sqrt{2}} = \frac{R}{R+h}$. $$R+h = \sqrt{2}R \Rightarrow h = (\sqrt{2}-1)R$$
Final Answer: (C)