An open cart of initial mass \(M_0\) is initially at rest on a frictionless horizontal surface. Sand drops vertically into the cart from a stationary overhead hopper at a constant mass rate of \(C = \dfrac{dm}{dt}\). A horizontal pulling force \(F(t)\) is applied to the cart such that it moves in a straight line with a constant horizontal acceleration \(a\). Which of the following expressions represents the magnitude of the horizontal force \(F(t)\) required to maintain this constant acceleration as a function of time \(t\)?