Question

If earth suddenly shrinks by one-third of its present radius, the acceleration due to gravity will be

• A. $\frac{2}{3}g$
• B. $\frac{3}{2}g$
• C. $\frac{4}{9}g$
• D. $\frac{9}{4}g$

Answer 1

Answer: (D)

$\frac{9}{4}g$

Answer 2

As, $g=\frac{GM}{R^{2}}$ i.e., $g \propto\frac{1}{R^{2}}$ Now radius of earth $R'=R-R/ 3=2R /3$ So $\frac{g'}{g}=\frac{R^{2}}{\left(2R/ 3\right)^{2}}$ $=\frac{9}{4}$ or $g'=\frac{9}{4}\,g$