Question

A spaceship of weight $39200kg-W$, lands on planet mars whose radius is $3.4\times 10^{6}m$ and mass is $6.42\times 10^{23}kg$ The weight of space ship on mars will be (surface tension of water $=7\times 10^{-2}N/m)$

• A. 5000 kg-W
• B. 10000 kg-W
• C. 15000 kg-W
• D. 20000 kg-W

Answer 1

Answer: (C)

The mass of spaceship
$m=\frac{39200}{9.8}=4000kg$
On earth; $g=\frac{GMm}{R^2}...(i)$
On mars, $g^{\prime }=\frac{G{M}^{\prime }m}{R^{\prime 2}}...(ii)$
$\therefore \frac{g^{\prime }}{g}=\frac{M^{\prime }}{M}\times \frac{R^2}{R^{\prime 2}}...(iii)$
Here $:R=6400km=6.4\times 10^{6}m$
$R^{\prime }=3.4\times 10^{6}m$
$R^{\prime }=3.4\times 10^{6}m$
$M=6.0\times 10^{24}kg,$
$M^{\prime }=6.42\times 10^{23}kg$
Putting the given values in eq (i)
$\therefore g^{\prime }=\frac{6.42\times 10^{23}\times {\left(6.4\times 10^6\right)}^2}{6\times 10^{24}\times {\left(3.4\times 10^6\right)}^2}\times 9.8$
$\Rightarrow g^{\prime }\approx 3.7m/se{c}^2$
Hence, the weight of spaceship on mars
$w^{\prime }=m{g}^{\prime }$
$=4000\times 3.7$
$=14800$
$\approx 15000kg$