The time derivative of a differentiable function \( g(q_i, t) \) is added to a Lagrangian \( L(q_i, \dot{q}_i, t) \) such that
\[
L' = L(q_i, \dot{q}_i, t) + \frac{d}{dt} g(q_i, t)
\]
where \( q_i \), \( \dot{q}_i \), \( t \) are the generalized coordinates, generalized velocities, and time, respectively. Let \( p_i \) be the generalized momentum and \( H \) the Hamiltonian associated with \( L(q_i, \dot{q}_i, t) \). If \( p_i' \) and \( H' \) are those associated with \( L' \), then the correct option(s) is(are):
