Question

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

• A. $6$N
• B. $20$N
• C. $40$N
• D. $80$N

Answer 1

Answer: (D)

$80$N

Radius of earth $=6400km\left(R_e\right)$

Radius of mars$=3200\left(R_m\right)$

Mass of mars $\left(M_m\right)=\frac{Massofearth\left(M_e\right)}{10}$

'g' on the surface of the earth $=\frac{G{M}_e}{R_e^2}$

So, 'g' on the surface of mars$=\frac{GMm}{R_m^2}=\frac{G{M}_e\times }{10R_e^2}=\frac{2g}{5}$

Weight on the surface of earth $=m{g}_{earth}=200$

Weight on the surface of mars$=m{g}_{mars}=m\left(\frac{2g_{earth}}{5}\right)=\frac{2}{5}\times 200=80N$