If the mass of the Earth were to double while its radius remained the same, what would happen to the acceleration due to gravity on its surface?

Solution

1. The acceleration due to gravity $g$ on the surface of a planet is given by the formula $g=\frac{GM}{R^2}$, where $M$ is the mass and $R$ is the radius.
2. If the mass $M$ is doubled to $2M$ while the radius $R$ remains constant, the new acceleration $g^{\prime }$ becomes $g^{\prime }=\frac{G(2M)}{R^2}$.
3. Simplifying the expression, we find $$\begin{array}{rl}{g}^{\prime }& =2\times \frac{GM}{R^2}\\ & =2g\end{array}$$.
4. Hence the answer is (C).