A Pulley with Radius R Is Free to Rotate on a Horizontal

Multiple Choice

A pulley with radius R is free to rotate on a horizontal fixed axis through its center. A string passes over the pulley. Mass m₁ is attached to one end and mass m₂ is attached to the other. The portion of the string attached to m₁ has tension T₁ and the portion attached to m₂ has tension T₂. The magnitude of the total external torque, about the pulley center, acting on the masses and pulley, considered as a system, is given by:

A) $\mid$ m₁ - m₂ $\mid$ gR
B) (m₁ + m₂) gR
C) $\mid$ m₁ - m₂ $\mid$ gR + (T₁ + T₂) R
D) (m₁ + m₂) gR + (T₁ - T₂) R
E) $\mid$ m₁ - m₂ $\mid$ gR + (T₂ - T₁) R