Question

Radius of Earth is $6400km$ and that of Mars is $3200km$ . Mass of Mars is $0.1$ that of Earth's mass. Then, the acceleration due to gravity on Mars is nearly

• A. $1m/s^2$
• B. $2.5m/s^2$
• C. $4m/s^2$
• D. $5m/s^2$

Answer 1

Answer: (C)

Acceleration due to gravity of a planet is
$g=\frac{GM}{R^2}$ where, $M=$ mass of planet
$R=$ radius of planet
$g_m=g_{\text{Mas }}=\frac{GMm}{R_m^2}$
$\Rightarrow g_e=g_{\text{Earth }}=\frac{GMe}{R_e^2}\frac{g_m}{g_e}$
$=\left(\frac{Mm}{Me}\right){\left(\frac{R_e}{R_m}\right)}^2$
$=(0.1){\left(\frac{6400}{3200}\right)}^2$
$=(0.1)(2{)}^2=4\times 10.1=0.4$
$\Rightarrow g_m=(0.4)(10)=4m/s^2$