Question

At a point very near to the earth's surface, the acceleration due to gravity is g. What will be the acceleration due to gravity at the same point if the earth suddenly shrinks to half its radius without any change in its mass?

• A. $2g$
• B. $4g$
• C. $g$
• D. $3g$

Answer 1

The correct option is B $4g$

Acceleration due to gravity on the earth's surface is $g=\frac{GM}{R^2}$

If earth suddenly shrinks to half its radius, the acceleration due to gravity becomes, $g^{\prime }=\frac{GM}{(R/2{)}^2}=4GM/R^2=4g$