Question

If the Earth were compressed in such a way that its mass remained the same, but the distance around the equator were just one-half what it is now, what would be the acceleration due to gravity at the surface of the Earth?

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

Answer 1

Answer: (E)

4g

Acceleration due to gravity $g=\frac{GM}{R^2}$ where $R$ is the distance of equator from the centre

New distance of equator from the centre $R^{\prime }=\frac{R}{2}$

Thus new acceleration due to gravity $g^{\prime }=\frac{GM}{(R/2{)}^2}=4g$