A block of mass M is pulled all along a horizontal frictionless surface through a rope of mass m. The horizontal force F is exerted to one end of the rope. (i) Illustrate that the rope should sag, even if only through an imperceptible amount. Then, supposing that the sag is negligible, determine (ii) the acceleration of rope and block, (iii) the force on the block from the rope, and (iv) the tension in the rope at its mid-point.