Question

The height at which the acceleration due to gravity becomes \(\frac{g}{4}\) in terms of \(R\) is [ \(R = \text{the radius of the earth}\) ]

• A. \(\frac{R}{\sqrt{2}}\)
• B. \(\text{R}\)
• C. \(\sqrt{2}R\)
• D. \(2R\)

Hint:

Formula: $g_h = g\left(\frac{R}{R+h}\right)^2$

Answer 1

The Correct Option is B

Concept: \[ g_h = g \left(\frac{R}{R + h}\right)^2 \]

Step 1: Given condition. \[ \frac{g}{4} = g \left(\frac{R}{R + h}\right)^2 \]

Step 2: Simplify. \[ \frac{1}{4} = \left(\frac{R}{R + h}\right)^2 \Rightarrow \frac{1}{2} = \frac{R}{R + h} \] \[ R + h = 2R \Rightarrow h = R \] Final Answer: Option (B)