The disc is removed and replaced with a pie-shaped wedge of the same mass m, so that the hinge is still initially held open at an angle \theta, as shown in the following figure. If the wedge is released from rest, what is its speed after it exits the launcher?
Answer Choices
A. \sqrt{\frac{\tau}{2 m \theta}}
B. \sqrt{\frac{4 \tau \theta}{m}}
C. \sqrt{\frac{\tau \theta^{2}}{2 m}}
D. \sqrt{\frac{2 \tau \theta}{m}}
E. \sqrt{\frac{2 \tau}{m \theta}}