1. A thin cord is wound around a homogeneous cylinder with mass mA and radius R. The cord extends horizontally from the cylinder to a pulley and then vertically downwards to a block B with mass mg. See the figure below. The pulley is massless and frictionless. The gravitational acceleration is ~g, and directed vertically downwards. The moment of inertia of the cylinder with respect to the axis through the center of the cylinder is IA = MAR. The cylinder rolls without slipping. A B (a) Express the instantaneous velocity VA of the center of mass of the cylinder in terms of its angular velocity WA. What is the relation between the velocity V of the center of mass of the cylinder, and the velocity of block B? (b) Give the instantaneous kinetic and potential energy for this system. (c) Determine the acceleration a of the center of mass of the cylinder and the tension in the cord.