The correct answer is option 1: buoyant force on the ball is larger than that of the nail due to their shapes.

When an object is submerged in a fluid, it experiences two main forces: its weight, which is the force of gravity acting on it, and the buoyant force, which is the upward force exerted by the fluid on the object.

In this scenario, the iron nail and iron ball have the same mass, so their weight is the same. However, the shapes of the objects are different. The iron ball is round and compact, while the nail has a long and thin shape.

The buoyant force on an object is determined by the volume of the object that is submerged in the fluid. In the case of the iron ball, its round shape allows a larger volume to be submerged, resulting in a larger buoyant force. On the other hand, the long and thin shape of the nail results in a smaller volume being submerged, and thus a smaller buoyant force.

Because the buoyant force is larger for the iron ball, it can counteract the weight of the object and make it float. In contrast, the smaller buoyant force on the nail is not enough to counteract its weight, causing it to sink.

Therefore, option