A) \[4.9\text{ }m/se{{c}^{2}}\]
B) \[8.9\text{ }m/se{{c}^{2}}\]
C) \[19.6\text{ }m/se{{c}^{2}}\]
D) \[29.4\text{ }m/se{{c}^{2}}\]
Correct Answer: C
Solution :
\[g=\frac{GM}{{{R}^{2}}}\,\,\,\,\,\,\,\,\therefore \,\,\,\,\,g\propto \frac{M}{{{R}^{2}}}\] According to problem \[{{M}_{p}}\,=\,\frac{{{M}_{e}}}{2}\,\,and\,\,{{R}_{p}}\,=\,\frac{{{\operatorname{R}}_{e}}}{2}\] \[\therefore \,\,\,\,\,\frac{{{g}_{p}}}{{{g}_{e}}}\,=\,\left( \frac{{{M}_{p}}}{{{M}_{e}}} \right)\,{{\left( \frac{{{\operatorname{R}}_{e}}}{{{R}_{p}}} \right)}^{2}}\,\,=\,\,\left( \frac{1}{2} \right)\,\,\times \,\,{{(2)}^{2}}=\,\,2\] \[\Rightarrow \,\,\,\,\,{{g}_{p}}\,\,=\,\,2{{g}_{e}}\,\,\times 9.8=19.6\,\,m/{{s}^{2}}\]
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