Question

The value of acceleration due to gravity (g) becomes \(\left(\frac{g}{3}\right)\) at height ' \(h\) ' above the earth's surface. If ' R ' is the radius of earth, the height h will be equal to

• A. \(\sqrt{3}\mathrm{R}\)
• B. 3 R
• C. \((\sqrt{3}-1)\mathrm{R}\)
• D. \((\sqrt{3}+1)R\)

Hint:

Use g' = g R squared over (R + h) squared.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
At height \(h\), \(g'=g\dfrac{R^{2}}{(R+h)^{2}}\).

Step 2: Set up
\(\dfrac{g}{3}=g\dfrac{R^{2}}{(R+h)^{2}}\Rightarrow(R+h)^{2}=3R^{2}\).

Step 3: Solve
\(R+h=\sqrt{3}R\Rightarrow h=(\sqrt{3}-1)R\).

Final Answer:
The height is \((\sqrt{3}-1)R\). \[ \boxed{\text{(C) }(\sqrt{3}-1)\mathrm{R}} \]