Question

The radius of the earth is about $6400$ km and that of mars is $3200$ km. Thus mars of the earth are about $10$ times the mass of mars. An object weighs $200N$ on the surface of the earth. Then its weight on the surface of mars will be

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

Answer 1

The correct option is A $80N$

Let the weight of the object on earth is W, and at mars be $W_m$, then
$\frac{W_m}{W_e}=\frac{g_m}{g_e}=\frac{\frac{{GM}_m}{R_m}}{\frac{{GM}_e}{R_e^2}}=\frac{M_m}{M_e},{\left(\frac{R_e}{R_m}\right)}^2=\frac{1}{10}\times {\left(\frac{6400}{3200}\right)}^2=\frac{4}{10}\Rightarrow W_m\frac{4}{10}{W}_e=\frac{4}{10}\times 200=80N$