I would like to know how to calculate the torque required to pull a 10kg weight over a pulley wheel measuring 10 inches in circumference

Remember that torque is equal to the force you must overcome times the distance from the center of the pulley to the point where that force is applied. So here you have a mass of 10Kg - multiply that mass by g (the gravitational constant) to get its weight, then multiply that by the radius of the pulley. The result is in Nt-cm, and is the torque required to exactly balance the torque caused by the weight of the object.