Question

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

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

Answer 1

Answer: (C)

Radius of earth $\left(R_{e}\right)=6400 km$;
Radius of mars $\left(R_{m}\right)=3200 km$;
Mass of earth $\left(M_{e}\right)=10$ and weight of the object on earth $\left(W_{e}\right)=200\, N$.
$\frac{W_{m}}{W_{e}}=\frac{m g_{m}}{m g_{e}}=\frac{M_{m}}{M_{e}} \times\left(\frac{R_{e}}{R_{m}}\right)^{2}=\frac{1}{10} \times(2)^{2} $
$=\frac{4}{10}=\frac{2}{5} $
or $ W_{m}=W_{e} \times \frac{2}{5}$
$=200 \times 0.4=80\, N $