A) 2% decrease
B) 2% increase
C) 1% increase
D) 1% decrease
Correct Answer: A
Solution :
Here: \[{{R}_{1}}=R\] (initial radius) \[{{R}_{2}}=R\,(1-0.01)\] (final radius) \[=0.99R\] Acceleration due to g \[g=\frac{GM}{{{R}^{2}}}\propto \frac{1}{{{R}^{2}}}\] Hence, \[\frac{{{g}_{1}}}{{{g}_{2}}}={{\left( \frac{{{R}_{2}}}{{{R}_{1}}} \right)}^{2}}={{\left( \frac{0.99R}{R} \right)}^{2}}=0.98\] or, \[{{g}_{2}}=\frac{{{g}_{1}}}{0.98}=1.02{{g}_{1}}\] Hence change in gravitational acceleration \[={{g}_{2}}-{{g}_{1}}=1.02{{g}_{1}}-{{g}_{1}}=0.02{{g}_{1}}=2%\]positive sign indicates increment.
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