Question

Height at which value of $g$ becomes one fourth to that on earth is

• A. $R$
• B. $2R$
• C. $\frac{3R}{2}$
• D. $4R$

Answer 1

The correct option is A

$R$

Explanation for the correct option(s):

(A): R

Acceleration due to gravity because of height $h$ can be calculated by using the formula: $g_h=g{\left[\frac{R}{R+h}\right]}^2$

It is given that $g_h$ becomes one-forth to that on earth i.e. $g_h=\frac{g}{4}$

$$\begin{gathered} g_h=g{\left[\frac{R}{R+h}\right]}^2 \\ \frac{g}{4}=g{\left[\frac{R}{R+h}\right]}^2 \\ {\left[\frac{R}{R+h}\right]}^2=\frac{1}{4} \\ \frac{R}{R+h}=\frac{1}{2} \\ 2R=R+h \\ h=R \end{gathered}$$

Hence, option (A) is correct.