Question

Mars has about ${\left(\frac{1}{10}\right)}^{th}$ as much mass as the Earth and its diameter is only half that of the earth. The acceleration of failing body on Mars is nearly:

• A. $9.8m{s}^{-2}$
• B. $1.96m{s}^{-2}$
• C. $3.92m{s}^{-2}$
• D. $4.9m{s}^{-2}$

Answer 1

The correct option is C $3.92m{s}^{-2}$

The acceleration due to gravity, $g=\frac{G{M}_e}{R_e^2}$

Where, $M_e$is the mass of earth

$R_e$is the radius of earth.

Given that,

Mass of mars, $M_m=\frac{1}{10}{M}_e$

Radius of mars, $R_m=\frac{D_e}{4}=\frac{2R_e}{4}=\frac{R_e}{2}$

Acceleration due to gravity is,

$g_m=\frac{G\frac{1}{10}{M}_e\times 4}{R_e^2}$

$g_m=\frac{4}{10}\frac{GM}{R_e^2}$

$g_m=\frac{4}{10}\times 9.8(g_{earth}=9.8m/s^2)$

$g_m=0.98m/s^2$

$g_m=3.92m{s}^{-2}$