Question

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

Answer: (C)

Acceleration due to gravity of a planet is
$g=\frac{G M}{R^{2}}$ where, $M =$ mass of planet
$R =$ radius of planet
$g_{m}=g_{\text {Mas }}=\frac{G M m}{R_{m}^{2}}$
$\Rightarrow g_{e} =g_{\text {Earth }}=\frac{G M e}{R_{e}^{2}} \frac{g_{m}}{g_{e}}$
$=\left(\frac{M m}{M e}\right)\left(\frac{R_{e}}{R_{m}}\right)^{2}$
$=(0.1)\left(\frac{6400}{3200}\right)^{2}$
$=(0.1)(2)^{2}=4 \times 10.1=0.4$
$\Rightarrow g_{m}=(0.4)(10)=4\, m / s ^{2}$