A) \[1\text{ }m/{{s}^{2}}\]
B) \[\text{2}\text{.5 }m/{{s}^{2}}\]
C) \[\text{4 }m/{{s}^{2}}\]
D) \[\text{5 }m/{{s}^{2}}\]
Correct Answer: C
Solution :
Acceleration due to gravity of a planet is \[g=\frac{GM}{{{R}^{2}}}\] where, M = mass of planet R = radius of planet \[{{g}_{m}}={{g}_{Mars}}=\frac{GMe}{R_{e}^{2}}\] \[\Rightarrow \] \[{{g}_{e}}={{e}_{Earth}}=\frac{GMe}{R_{e}^{2}}\] \[\frac{{{g}_{m}}}{{{g}_{e}}}=\left( \frac{Mm}{Me} \right){{\left( \frac{{{R}_{e}}}{{{R}_{m}}} \right)}^{2}}=(0.1){{\left( \frac{6400}{3200} \right)}^{2}}\] \[=(0.1){{(2)}^{2}}=4\times 10.1=0.4\] \[\Rightarrow \] \[{{g}_{m}}=(0.4)(10)=4m/{{s}^{2}}\]
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