Q. If the diameter of mars is 6760 km and mass one-tenth that of earth. The diameter of earth is 12742 km. If acceleration due to gravity on earth is $9.8\ ms^{- 2}$, the acceleration due to gravity on mass is
A) $34.8\ ms^{- 2}$
B) $2.84\ ms^{- 2}$
C) $3.48\ ms^{- 2}$
D) $28.4\ ms^{- 2}$
Explanation
(c) $g = \frac{GM}{R^{2}}$
So, $\frac{g_{M}}{g_{E}} = \left( \frac{M_{M}}{M_{E}} \right) \times \left( \frac{R_{E}}{R_{M}} \right)^{2} = \frac{1}{10} \times \left( \frac{12742}{6760} \right)^{2}$
$\therefore\frac{g_{M}}{g_{E}} = 0.35 \Rightarrow g_{M} = 9.8 \times 0.35 = 3.48\ ms^{- 2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.