Question

If density of a planet is double that of the earth and the radius $1.5$ times that of the earth, the acceleration due to gravity on the surface of the planet is

• A. $\frac{3}{4}$ times that on the surface of the earth
• B. $3$ times that on the surface of the earth
• C. $\frac{4}{3}$ times that on the surface of the earth
• D. $6$ times that on the surface of the earth

Answer 1

Answer: (B)

Acceleration due to gravity on the surface of a planet is
given by, $g=\frac{GM}{R^2}$
$M\to$ Mass of the planet
$R\to$ Radius of the planet
Also, $M=\frac{4}{3}\pi R^3\times \rho$
$\Rightarrow g=\frac{G}{R^2}\times \frac{4}{3}\pi R^3\rho =\frac{4}{3}\rho G\pi R$
$\rho \to$ Density of the planet.
$\Rightarrow$ Acceleration due to gravity $\alpha \rho R$
$\Rightarrow \frac{g_{\text{planet }}}{g_{\text{earth }}}=\frac{2{\rho }_e\times 1.5R_e}{{\rho }_e\times R_e}=3$
$\Rightarrow$ Acceleration due to gravity on the surface of planet is 3 times that on the surface of earth.