A) \[19.6\,m{{s}^{-2}}\]
B) \[9.8\,m{{s}^{-2}}\]
C) 4.9 \[m{{s}^{-2}}\]
D) 2.45 \[m{{s}^{-2}}\]
Correct Answer: A
Solution :
[a] Acceleration due to gravity (g?) on the planet is given by, g' = \[\frac{GM}{{{R}^{2}}}\], where M is mass and R is radius of the planet. We have, \[M=\frac{{{M}_{e}}}{2}\] and \[R=\frac{{{R}_{e}}}{2}\] \[\therefore g'=\frac{\frac{G{{M}_{e}}}{2}}{{{\left( \frac{{{R}_{e}}}{2} \right)}^{2}}}=\frac{2G{{M}_{e}}}{{{R}_{e}}^{2}}=2{{g}_{e}}\] \[=2\times 9.8=19.6\,\,\,m{{s}^{-2}}\]
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