Two wooden boxes A and B of masses 6 kg and 4 kg respectively are connected by a light inextensible string that passes over a small frictionless pulley fixed at the edge of a smooth horizontal table. Box A is on the table, while box B hangs vertically over the side, as shown in the description. The string and pulley have negligible mass. Air resistance is negligible.
a. (a) Taking downward direction for box B as positive, write the equations of motion for each box.
b. (b) By eliminating the tension in the string, derive an expression for the common acceleration of the system in terms of g and the given masses.
c. (c) Calculate the numerical values of (i) the acceleration of the boxes and (ii) the tension in the string.