A) \[\text{19}.\text{6 m}/{{\text{s}}^{\text{2}}}\]
B) \[\text{9}.\text{8 m}/{{\text{s}}^{\text{2}}}\]
C) \[\text{4}.\text{9 m}/{{\text{s}}^{\text{2}}}\]
D) \[\text{2}.\text{45 m}/{{\text{s}}^{\text{2}}}\]
Correct Answer: A
Solution :
From relation, \[g=\frac{GM}{{{r}^{2}}}\] \[\frac{{{g}_{planet}}}{{{g}_{earth}}}=\frac{G{{M}_{p}}/R_{p}^{2}}{G{{M}_{e}}/R_{e}^{2}}=\frac{{{M}_{p}}}{{{M}_{e}}}{{\left( \frac{{{R}_{e}}}{{{R}_{p}}} \right)}^{2}}\] \[=\left( \frac{1}{2} \right){{\left( \frac{2}{1} \right)}^{2}}=\frac{4}{2}=2\,\,or\,\,{{g}_{p}}=2\] \[{{g}_{e}}=2\times 9.8\,\,or\,\,{{g}_{p}}=19.6\,m/{{s}^{2}}\]
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