Question

The height at which the acceleration due to gravity becomes $\frac{g}{9}$, is

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

Answer 1

The correct option is A

$2R$

Step 1: Formula used

Acceleration due to gravity at a height $h$ is given as

$g\text{'}=g{\left(\frac{R}{R+h}\right)}^2$

Here, $g$ is the acceleration due to gravity on the surface of the earth, and $R$ is the radius of the earth.

Step 2: According to the question if we put

$g\text{'}=\frac{g}{9}$

Then we get

$\frac{g}{9}=g{\left(\frac{R}{R+h}\right)}^2$

$\frac{1}{3}=\left(\frac{R}{R+h}\right)$

Step 3: Final answer

$h=2R$

Thus, the correct option is (a).