Two forces each of magnitude F act perpendicular to each other. The angle made by the resultant force with the horizontal will be:

Explanation

(a) 30°: If two forces of equal magnitude act perpendicular to each other, the resultant force will be equal in magnitude to the individual forces. In this case, the resultant force will also be perpendicular to the individual forces. Therefore, the angle made by the resultant force with the horizontal will be 90°, not 30°. So, this option is not correct. (b) 45°: When two forces of equal magnitude act perpendicular to each other, the resultant force will be the vector sum of the individual forces. The magnitude of the resultant force will be equal to the square root of the sum of the squares of the individual forces. In this case, since the forces are equal, the magnitude of the resultant force will also be equal to the magnitude of the individual forces. The angle made by the resultant force with the horizontal will be 45°. So, this option is correct. (c) 60°: If two forces of equal magnitude act perpendicular to each other, the resultant force will not make an angle of 60° with the horizontal. The correct angle in this case is 45°, as explained in option (b). So, this option is not correct. (d) 90°: When two forces of equal magnitude act perpendicular to each other, the resultant force will be the vector sum of the individual forces. The magnitude of the resultant force will be equal to the square root of the sum of the squares of the individual forces. In this case, since the forces are equal, the magnitude of the resultant force will also be equal to the magnitude of the individual forces. The angle made by the resultant force with the horizontal will be 45°, not 90°. So, this option is not correct. In summary, the correct option is (b) - the angle made by the resultant force with the horizontal will be 45°.