Final answer:
The correct instrument used for placing elastic ligatures is B) Cotton pliers, which help in accurately positioning the ligatures on orthodontic brackets.
Step-by-step explanation:
In the placement of elastic ligatures, which are small rubber bands used in orthodontics, the appropriate instrument that may be used is B) Cotton pliers. Elastic ligatures are typically placed around the brackets on orthodontic braces to hold the archwire in place. Dental mirrors (A) are primarily for visualization and indirect vision during examinations and procedures, not for placing ligatures. X-ray machines (C) are for imaging and diagnostic purposes. Ultrasonic scalers (D) are for removing tartar and plaque from teeth, not for orthodontic ligature placement. Therefore, the correct instrument to use for placing elastic ligatures is cotton pliers, which allow the orthodontist or dental assistant to grasp and place the ligatures accurately on the brackets.