Two forces act an angle of 120°. If the greater force is 50 kg and their resultant is perpendicular to the smaller force, the smaller force is A. 20 kg B. 25 kg C. 30 kg D. 35 kg

The correct answer is $\boxed{\text{B) 25 kg}}$.

Let $F_1$ be the greater force and $F_2$ be the smaller force. We know that $F_1 = 50$ kg and that the resultant force is perpendicular to the smaller force. This means that the angle between $F_1$ and $F_2$ is $120^\circ$.

We can use the law of cosines to solve for $F_2$:

$$F_2^2 = F_1^2 + F_2^2 – 2F_1F_2\cos(120^\circ)$$

$$F_2^2 = 50^2 + F_2^2 – 2(50)(F_2)(-0.5)$$

$$F_2^2 = 625 + 2F_2^2 + 50F_2$$

$$F_2^2 – 50F_2 – 575 = 0$$

$$(F_2 – 25)(F_2 + 23) = 0$$

$$F_2 = 25\text{ kg}$$ or $$F_2 = -23\text{ kg}$$

Since force is a vector, it has both magnitude and direction. The direction of the smaller force is unknown, so we cannot determine its magnitude. However, we can say that the magnitude of the smaller force is greater than or equal to 25 kg.