Consider three cases. Case 1: A person holds her arm at an angle of 30°30° above the horizontal (hand is higher than shoulder). Case 2: A person holds her arm straight out parallel to the ground. Case 3: A person holds her arm at an angle of 30°30° below the horizontal (hand is lower than shoulder). In which of the cases is the torque about the shoulder due to the weight of the arm the greatest?

Case 2: A person holds her arm straight out parallel to the ground.

Explanation:

When we are measuring torque, we must multiply the force that causes the torque times the perpendicular distance to the specified point. In other words, the torque for 3 cases where the force is equal will vary depending on the perpendicular distance.

Since holding your arm straight out parallel to the ground results in your arm being totally perpendicular to your body, the torque will be greatest at that point. When your arm is at an angle, the perpendicular distance will be smaller.

whichever one it is, it's definitely not one that you included on the list you provided.