A) increased 2%
B) decreased 1.5%
C) increased 1%
D) decreased 1%
Correct Answer: A
Solution :
From law of gravitation. \[F=G\frac{{{M}_{e}}m}{R_{e}^{2}}\] ?(i) Also from Newton's law \[F=mg\] Equating Eqs. (i) and (ii), we get \[g=\frac{G{{M}_{e}}}{R_{e}^{2}}\] \[\frac{{{g}_{1}}}{{{g}_{2}}}={{\left( \frac{{{R}_{2}}}{{{R}_{1}}} \right)}^{2}}\] \[={{\left( \frac{0.99R}{R} \right)}^{2}}\] \[\frac{{{g}_{1}}}{{{g}_{2}}}=0.98\] \[\therefore \] \[{{g}_{2}}=\frac{{{g}_{1}}}{0.98}=1.02\,{{g}_{1}}\] Hence, change in acceleration due to gravity \[={{g}_{2}}-{{g}_{1}}=1.02{{g}_{1}}-{{g}_{1}}=0.02{{g}_{1}}=2%{{g}_{1}}\] Since, sign is positive, acceleration due to gravity will increase by 2%
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