Question

If the radius of the Earth were increased by a factor of $2$ and its mass remained the same, then the acceleration due to gravity on the Earth would

• A. reduce by factor $4$
• B. reduce by factor $2$
• C. not change
• D. none of the above

Answer 1

The correct option is A reduce by factor $4$

In general we know that, force of gravity between two objects (M and m) at a distance r is given by:

$F=G\frac{Mm}{r^2}$

Also $F=mg$

$\therefore g=\frac{GM}{r^2}$

If the radius of the Earth were increased by a factor of 2 and its mass remained the same, then the acceleration due to gravity on the Earth would be:

$g^{\prime }=\frac{GM}{(2r{)}^2}=\frac{GM}{4r^2}=\frac{g}{4}$