Question

The radius of earth is about $6400km$ and that of mars is about $3200km$. The mass of the earth is about $10$ times the mass of mars. A object weighs $200N$ on earths surface, then its weight on the surface of mars will be :

• A. 80 N
• B. 40 N
• C. 8N
• D. 20 N

Answer 1

Answer: (A)

From law of gravitation, the force of attraction on body due to earth is
$F=\frac{GMm}{R^2}=mg=w_e$
Given, $R_e=6400km,R_m=3200km$,
$M_e=10M_m{w}_e=200N$
$\therefore \frac{w_m}{w_e}=\frac{M_m}{M_e}{\left(\frac{R_e}{R_m}\right)}^2$
$\Rightarrow w_m=\frac{M_m}{M_e}{\left(\frac{R_e}{R_m}\right)}^2\times w_e$
$w_m=\frac{1}{10}{\left(\frac{6400}{3200}\right)}^2\times 200$
$w_m=80N$ .