Lagrange's equation is
$\begin{align*}\frac{\partial L}{\partial q_n} = \frac{d}{dt} \frac{\partial L}{\partial \dot{q}_n}\end{align*}$
The generalized momentum $p_n$ is defined as
$\begin{align*}p_n = \frac{\partial L}{\partial \dot{\theta}}\end{align*}$
Therefore, if
$\begin{align*}\frac{\partial L}{\partial q_n} = 0\end{align*}$
then
$\begin{align*}\frac{d p_n}{dt} = 0\end{align*}$
Therefore, answer (B) is correct.

Solution to 1992 Problem 43