Question

The acceleration of a body due to the attraction of the earth $\left(\text{radius}R\right)$ at a distance $2R$ from the surface of the earth is ( $g=$ acceleration due to gravity at the surface of the earth)

• A. $g$
• B. $\frac{g}{4}$
• C. $\frac{g}{9}$
• D. $\frac{g}{3}$

Answer 1

The correct option is C $\frac{g}{9}$

Formula used: $g^{\prime }=g{\left(\frac{R}{R+h}\right)}^2$
Given,
$h=2R$
Acceleration due to gravity at height $h$ is given by
$g^{\prime }=g{\left(\frac{R}{R+h}\right)}^2$
$\frac{g^{\prime }}{g}={\left(\frac{R}{R+h}\right)}^2={\left(\frac{R}{R+2R}\right)}^2=\frac{1}{9}$

$\therefore g^{\prime }=\frac{g}{9}$
Final Answer: (a)