Question

The radius of Earth is about $6400\text{km}$ and that of Mars is $3200\text{km}$. The mass of the Earth is about $10$ times the mass of Mars. If an object weighs $200\text{N}$ on the surface of Earth, its weight on the surface of Mars will be

• A. $20\text{N}$
• B. $8\text{N}$
• C. $80\text{N}$
• D. $40\text{N}$

Answer 1

The correct option is C $80\text{N}$

Given:
Radius of earth $R_e=6400\text{km}$
Radius of earth $R_M=3200\text{km}$

Let, mass of Mars $=M_M$
mass of earth $=M_e$

Weight of the particle of mass $m$ at the surface of the earth is

$W_e=m{g}_e=\frac{mG{M}_e}{R{{}_e}^2}.......\left(1\right)$

Similarly, weight at the surface of Mars

$W_M=m{g}_M=\frac{mG{M}_M}{R{{}_M}^2}......\left(2\right)$

dividing eq. (1) to (2)

$\frac{W_e}{W_M}=(\frac{M_e}{M_M})(\frac{R_M}{R_e}{)}^2$

$\Rightarrow \frac{200}{W_M}=10\times (\frac{1}{2}{)}^2[\therefore \frac{M_e}{M_M}=10]$

$\Rightarrow W_M=\frac{200\times 4}{10}=80\text{N}$

Hence, option $\left(c\right)$ is correct.