A thin cart, of mass M, is lying at rest, at the origin of a narrow straight horizontal track. A force F ( = F(x)), is applied on it, at an angle θ to the horizontal. The acceleration, produced in the cart, increases in direct proportion to the distance, x, moved by the cart. If the coefficient of friction, between the cart and the road, is μ, the work done, by the force F, in moving the cart through a distance L, would equal.
(1) \(\frac{MLCos\theta}{2(cos\theta-μsin\theta)}[a_0L+2μg]\)
(2) \(\frac{MLCos\theta}{(cos\theta-μsin\theta)}[2a_0L+μg]\)
(3) \(\frac{MLCos\theta}{(cos\theta-μsin\theta)}[2a_0L+μg]\)
(4) \(\frac{ML}{2(cos\theta-μsin\theta)}[a_0L+2μg]\)