Question

If the Earth were compressed in such a way that its mass remained the same, as a result of this compression distance around the equator reduced half of the actual, what would be the new acceleration due to gravity at the surface of the Earth?

• A. $g/4$
• B. $g/2$
• C. $g$
• D. $2g$
• E. $4g$

Answer 1

The correct option is E $4g$

The value of $g$ is given by $g=\frac{GM}{R^2}$

where $G=$universal gravitational constant ,$M=$mass of planet(here earth) it is given constant , $R=$radius of planet (earth)

now if radius is halved $=R/2$

then $g^{\prime }=\frac{GM}{{\left(R/2\right)}^2}=4\frac{GM}{R^2}$

or $g^{\prime }=4g$