Step 1: Understanding the Concept:
A painful arc is pain that appears only in the middle of shoulder abduction, about $60^{\circ}$ to $120^{\circ}$, and goes away again once the arm rises further. It happens because a structure gets pinched under the acromion in that window.
Step 2: Key Formula or Approach:
Ask, for each option, is there a structure still there to get pinched during that mid-range window? If yes, expect a painful arc. If the structure is gone or fully torn through, there is nothing left to catch, so no true arc.
Step 3: Detailed Explanation:
Tendinitis of supraspinatus keeps the tendon intact but inflamed, so it still rubs and pinches under the acromion during that arc, giving pain.
Bursitis of the subacromial bursa places swollen, tender tissue right where the pinch happens, so the arc shows up again.
A fractured greater tuberosity leaves a bony bump that still catches under the acromion through that same range, so the arc pattern is preserved.
A complete tear of supraspinatus is different: the tendon is torn all the way through, so nothing bridges the gap to get trapped under the acromion in that mid-range. Instead the shoulder shows weak or absent active abduction and a drop-arm sign, not the classic mid-range-only pain.
Step 4: Final Answer:
Because nothing is left intact to impinge, a complete supraspinatus tear does not give the classic painful arc.
$\boxed{\text{Complete supraspinatus tear}}$