Question

Imagine a planet having the same density as that of the earth but radius is three times the radius of the earth. If acceleration due to gravity on the surface of the earth is g and that on the said planet is g', then

• A. $g^{\prime }=\frac{g}{9}$
• B. $g^{\prime }=9g$
• C. $g^{\prime }=\frac{g}{27}$
• D. $g^{\prime }=3g$

Answer 1

Answer: (D)

$g^{\prime }=3g$

The acceleration due to gravity on earth's surface is
$g=\frac{GM}{R^2}$
$g=\frac{G\rho V}{R^2}$ ................................................(1)
Where, $G$ is the gravitational constant, $M$ is mass of earth, $R$ is radius of earth, $\rho$ is the density and $V$ is the volume of earth.

$V=4/3\times \pi \times R^3$

Putting this value in (1), we get

$g\propto R$

$\frac{g}{g^{\prime }}=\frac{R}{3R}$

$\therefore g^{\prime }=3g$