Question

The radius of earth is about 6400 km and that of Mars is 3200 km. The mass of the earth is about 10 times the mass of Mars. An object weighs 200 N on the surface of Earth. Its weight on the surface of mars will be:

• A. 20 N
• B. 8 N
• C. 80 N
• D. 40 N

Answer 1

Answer: (C)

Radius of earth $R_e=6400$ and that of Mars is $R_m=3200$ so $R_e=2R_m$

And if mass of earth be $M_e$ and that of Mars is $M_m$ then $M_e=10M_m$

Value of g on mars $g_m=\frac{G{M}_m}{R_m^2}$

and that on earth is $g_e=\frac{G{M}_e}{R_e^2}=\frac{G\times 10M_m}{4\times R_m^2}=2.5\frac{G{M}_m}{R_m^2}$ or $g_m=g_e/2.5$

Weight on earth is $200N$ so mass $200/g_e$

Now weight on Mars will be $mass\times g_m=\left(200/g_e\right)\times g_m=200\times \frac{g_m}{g_e}=200/2.5=80N$

Option C is correct.