Final answer:
The maximum torque on a ball projected at an angle occurs at the highest point of its trajectory because the horizontal distance (lever arm) from the point of projection to the ball is at its maximum, and the gravitational force acts as a constant force.
Step-by-step explanation:
The question you're asking about involves understanding the concept of torque in projectile motion. When dealing with an object projected at an angle, such as a ball, torque is the product of the force applied to the ball and the perpendicular distance from the pivot point to the line of action of the force. In the absence of any external forces other than gravity, like air resistance, the only force acting on the ball when it is at the highest point of its trajectory will be gravity, which acts downward. Hence, at the highest point, the horizontal distance from the point of projection (assume point O is at the same level as the launching point and directly below the ball at its peak) to the ball is maximum, and therefore, the torque about point O due to gravity would also be maximum.
If we look at the options provided, a) The torque is maximum when the ball is at the highest point of its trajectory appears to be the correct choice. Since the horizontal distance is maximized at the highest point, the product of this distance (which acts as the lever arm) and the gravitational force (which is constant) will result in the maximum torque at this point. The torque is not independent of the position of the ball, nor is it maximal at the lowest point or the midpoint of its trajectory.