Question

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

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

Answer 1

Answer: (A)

$80N$

Let the weight of the object at Earth is $W_e$, and at Mars be $W_m$.

Then, $\frac{W_m}{W_e}=\frac{g_m}{g_e}=\frac{\frac{G{M}_m}{R_m^2}}{\frac{G{M}_e}{R_e^2}}=\frac{M_m}{M_e}.(\frac{R_e}{R_m}{)}^2$
$=\frac{1}{10}\times (\frac{6400}{3200}{)}^2=\frac{4}{10}$
$\Rightarrow W_m=\frac{4}{10}{W}_e=\frac{4}{10}\times 200=80N.$