The radius of the Earth is 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 200N on the surface of the Earth. Its weight on the surface of mars will be:

Weight is nothing more than the force that an item applies to the planet as a result of its gravitational pull. Varying planets experience gravity-related acceleration at different rates. It is provided by, $g=\frac{G{m}_e}{r_e^2}$. Take the ratio of the acceleration brought on by earth's gravity relative to mars in order to determine g on mars. To get the object's mass on Mars, multiply this amount by its mass.
In terms of the gravitational constant, the acceleration brought on by gravity is equal to:
$\Rightarrow g=\frac{G{m}_e}{r_e^2}\dots \text{ (1) }$
$\mathrm{G}=$ gravitational constant
$M=$ mass of the earth $=10\mathrm{x}$mass of mars
$\mathrm{R}=$ radius of the earth
According to the gravitational constant, the acceleration caused by gravity on Mars is:
$\Rightarrow g^{\text{'}}=\frac{G{m}_m}{{r_m}^2}\dots \left(2\right)$
$\Rightarrow m_m=$ mass of mars

$\Rightarrow r_m=$ radius of mars
Dividing 2 by 1
$\Rightarrow \frac{g^{\text{'}}}{g}=\frac{\frac{G{m}_m}{r_m^2}}{\frac{G{m}_e}{r_e^2}}$
$\Rightarrow \frac{g^{\text{'}}}{g}=\frac{m_m{r}_e^2}{r_m^2{m}_e}$
$\Rightarrow \frac{g^{\text{'}}}{g}=\frac{m_m{6400}^2}{{3200}^{2}10m_m}$
$\Rightarrow \frac{g^{\text{'}}}{g}=\frac{2^2}{10}$

Consequently, on Mars, the magnitude of the acceleration caused by gravity is:$0.4 \mathrm{g}$
Weight of a thing in mass $200 \mathrm{N}$ on earth is $=200/\mathrm{g}$
$\Rightarrow M=\frac{200}{g}$
Weight of a thing with mass of $\frac{200}{g}$ on Mars would be:
$\Rightarrow M{g}^{\text{'}}=\frac{200g^{\text{'}}}{g}$
$\Rightarrow 200\times 0.4=80 \mathrm{N}$

Hence, the correct answer is option C.