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# If radius of the earth were to shrink by one percent, its mass remaining same the value of g on the earth's surface would

$a) increase\; by\; 0.5 \% \\ b) increase\; by\; 2 \% \\ c) decrease\; b\; 0.5 \% \\ d) decrease\; by\; 2 \%$

$g= \large\frac{GM}{R^2}$
$\large\frac{dg}{g}$$=-2 \large\frac{dR}{R} given \large\frac{dR}{R}$$=-1 \%$
$=>\large\frac{dg}{g}$$=2 \%$
$\therefore$ g increases by $2 \%$
Hence b is the correct answer.
edited Jun 26, 2014