Question

The radius of earth is about $6400\, km$ and that of mars is about $3200\, km$. The mass of the earth is about $10$ times the mass of mars. A object weighs $200\, N$ 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, $R_{e}=6400\,km,\,R_{m}=3200\,km$,
$M_{e}=10\,M_{m}\,w_{e}=200\,N$
$\therefore \frac{w_{m}}{w_{e}}=\frac{M_{m}}{M_{e}}{{\left( \frac{R_{e}}{R_{m}} \right)}^{2}}$
$\Rightarrow w_{m}=\frac{M_{m}}{M_{e}}{{\left( \frac{R_{e}}{R_{m}} \right)}^{2}}\times w_{e}$
$w_{m}=\frac{1}{10}{{\left( \frac{6400}{3200} \right)}^{2}}\times 200$
$w_{m}=80\,N$ .