Final answer:
The magnitude of the gravitational field at the center of a square due to four identical masses placed at its corners is zero because the symmetrical vector contributions cancel each other out.
option A is the correct
Step-by-step explanation:
The question is asking for the magnitude of the gravitational field at the center of a square due to four identical masses placed at its corners. To solve this, we'll use the principle that a gravitational field is a vector quantity and we'll need to add the vectors originating from the mass at each corner of the square.
At the center of the square, the contributions of each mass to the gravitational field not only have the same magnitude but also are directed along the diagonals of the square toward each mass. Since the vectors are symmetrical, their horizontal and vertical components will cancel each other out. This leaves us with a net gravitational field of zero at the center of the square, as the vector contributions from opposing corners will have the same magnitude but opposite direction.
Therefore, we conclude that the magnitude of the gravitational field at the center of the square is option (a) 0.