If the mass of a planet is doubled and its radius is also doubled, what happens to the acceleration due to gravity on its surface?

Solution

1. The acceleration due to gravity on a planet's surface is given by the formula $g=\frac{GM}{R^2}$.
2. When the mass $M$ is doubled to $2M$ and the radius $R$ is doubled to $2R$, the new acceleration $g^{\prime }$ becomes $g^{\prime }=\frac{G(2M)}{(2R{)}^2}$.
3. Simplifying the expression, we get $$\begin{array}{rl}{g}^{\prime }& =\frac{2GM}{4R^2}\\ & =\frac{1}{2}\left(\frac{GM}{R^2}\right)\\ & =\frac{1}{2}g\end{array}$$.
4. Hence the answer is (A).