We use the formula
$\begin{align*}E^2 = m^2 c^4 + p^2 c^2\end{align*}$
We are given that $E = 100 m c^2$ , therefore
$\begin{align*}p = m c \sqrt{10000 - 1} \approx \boxed{100 mc}\end{align*}$
Therefore, answer (D) is correct.

Solution to 1992 Problem 70