Question

Assuming the mass of Earth to be ten times the mass of Mars and its radius to be twice the radius of Mars and the acceleration due to gravity on the surface of Earth to be $10 \, m/s^{-2} ,$ the acceleration due to gravity on the surface of Mars is given by

• A. $0.2 \, m/s^{-2}$
• B. $0.4 \, m/s^{-2}$
• C. $2 \, m/s^{-2}$
• D. $5\, m/s^{-2}$
• E. $4\, m/s^{-2}$

Answer 1

Answer: (E)

Given, mass of earth $=10 \times M_{m}$
Where, $M_{m}=$ Mass of mars
Radius of earth $=2\, R_{m}$
Where, $R_{m}=$ radius of mass
and $g=\frac{G M}{R^{2}}$
Let gravity on the surface of mass is $g_{m}$
$\therefore \frac{g_{m}}{g_{E}}=\frac{M_{m}}{M_{E}} \times\left(\frac{R_{E}}{R_{m}}\right)^{2} $
$g_{m}=g_{e} \times \frac{M_{m}}{M_{E}}\left(\frac{R_{E}}{R_{m}}\right)^{2}$
$=10 \times \frac{M_{m}}{10\, M_{m}}\left(\frac{2 R_{m}}{R_{m}}\right)^{2}=4 \,m / s ^{2}$