What is the value of the acceleration due to gravity at the center of the Earth?

Solution

1. The acceleration due to gravity $g^{\prime }$ at a distance $r$ from the center of the Earth is given by the formula $g^{\prime }=g\frac{r}{R}$, where $R$ is the radius of the Earth.
2. At the center of the Earth, the distance from the center is $r=0$.
3. Substituting $r=0$ into the formula, we get $$\begin{array}{rl}{g}^{\prime }& =g\frac{0}{R}\\ & =0\end{array}$$.
4. Hence the answer is (B).