A) \[0.49\,\,m/{{s}^{2}}\]
B) \[4.9\,\,m/{{s}^{2}}\]
C) \[0.98\,\,m/{{s}^{2}}\]
D) \[9.8\,\,m/{{s}^{2}}\]
Correct Answer: A
Solution :
Mass of the earth\[{{M}_{e}}=80\,\,{{M}_{p}}\] Diameter of earth\[{{D}_{e}}=2\,\,{{D}_{p}}\] or radius of the earth\[{{R}_{e}}=2\,\,{{R}_{p}}\] Gravitational acceleration is \[g=\frac{GM}{{{R}^{2}}}\propto \frac{M}{{{R}^{2}}}\]or\[\frac{{{g}_{e}}}{{{g}_{p}}}=\frac{{{M}_{e}}}{{{M}_{p}}}\times {{\left( \frac{{{R}_{p}}}{{{R}_{e}}} \right)}^{2}}\] \[\frac{{{g}_{e}}}{{{g}_{p}}}=\frac{80\,{{M}_{p}}}{{{M}_{p}}}\times {{\left( \frac{{{R}_{p}}}{2{{R}_{p}}} \right)}^{2}}=80\times \frac{1}{4}=20\] So, \[{{g}_{p}}=\frac{{{g}_{e}}}{20}=\frac{9.8}{20}=0.49\,\,m/{{s}^{2}}\]
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