Please see attachments.
ratio of radii,
rB/rC = rA/rC = 4/10 = 2/5
At the circumference of the A, B and C, the linear velocity, tangential acceleration and linear displacement will be same.
wA/wC (ratio of angular velocities of A and C)
= alpha(A)/alpha(C) (ratio of angular accelerations of A and C)
= d_theta(A)/d_theta(C) (ratio of angular displacement of A and C)
= rC/rA = 5/2 = 2.5
Torque on B (TB) = 6.75 lb.ft = 6.75*32 lb.ft^2/s^2
Work done by torque = T*d_theta = change ...
The solution is given equationally.