Sol. Let us write the equations of motion for m 1 and m 2 . First, the torque equations are

…..(i)

Now, the sum of forces of m 2 is given by :

m 2 g – T = m 2 a …..(ii)

Another equation is obtained using the relation linking the angular accelerations, α 1 and α 2

α = α 1 R 1 + α 2 R 2 …..(iii)

Note that m 2 rotates in the same direction as m 1 , and therefore, the linear accelerations sum. Now we have a set of four equations for four variables. Solving the set we find :

for the linear acceleration :

a = …..(iv)

for the angular accelerations :

…..(v)

and for the tension in the string:

T = g …..(vi)