Question

ACCELERATION DUE TO GRAVITY OF THE EARTH
Radius of earth is 6400 km and that of mars is 3200 km. Mass of mars is 0.1 that of earth's mass. Then the acceleration due to gravity on mars is nearly.

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

Answer 1

The correct option is C $4{m/s}^2$

If $M_e,R_e$ be the mass and radius of earth and $M_m,R_m$ be the corresponding quantities of mars, then Acceleration due to gravity on earth is $g_e=\frac{G{M}_e}{R_e^2}$ ....(i)
and that on mass is $g_m=\frac{G{M}_m}{R_m^2}$ .....(ii)
Dividing eqn. (ii) by eqn.(i), we get
$\frac{g_m}{g_e}=\left(\frac{M_m}{M_e}\right){\left(\frac{R_e}{R_m}\right)}^2$ or $g_m=g_e\left(\frac{M_m}{M_e}\right){\left(\frac{R_e}{R_m}\right)}^2$

Here, $g_e=9.8{m/s}^2,M_m=0.1M_e$

$R_e=6400km,R_m=3200km$

$\therefore g_m=\left(9.8{m/s}^2\right)\left(\frac{0.1M_e}{M_e}\right){\left(\frac{6400km}{3200km}\right)}^2$

$=\left(9.8{m/s}^2\right)\left(0.1\right)\left(4\right)=4{m/s}^2$