A) 5000 kg-W
B) 10000 kg-W
C) 15000 kg-W
D) 20000 kg-W
Correct Answer: C
Solution :
The mass of spaceship \[m=\frac{39200}{9.8}=4000\,kg\] On earth, \[\frac{GMm}{{{R}^{2}}}\] ...(i) On mars, \[g=\frac{GMm}{{{R}^{2}}}\] ?(ii) \[\therefore \] \[\frac{g}{g}=\frac{M}{M}\times \frac{{{R}^{2}}}{R{{}_{2}}}\] ?(iii) Here: \[R=6400\,km=6.4\,\times {{10}^{6}}\,m,\] \[R=3.4\,\times {{10}^{6}}m\] \[M=6.0\times {{10}^{24}}\,kg,\,M=6.42\,\times {{10}^{23}}\,kg\] Putting the given values m eq (i) \[\therefore \] \[g=\frac{6.42\times {{10}^{23}}\times {{(6.4\times {{10}^{6}})}^{2}}}{6\times {{10}^{24}}\times {{(3.4\times {{10}^{6}})}^{2}}}\times 9.8\] \[\Rightarrow \] \[g\approx 3.7\,m/{{\sec }^{2}}\] Hence, the weight of spaceship on mars \[w=mg\] \[=4000\times 3.7\] \[=14800\,\approx 15000\,kg\]
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