two forces F1 and F2 acting at a point have a resultant F. If F2 is doubled, F is also doubled. If F2 is reversed in direction, then also F is doubled, then

options A. F1:F=1:1 B. F2:F=root3:root2
C. F1:F2=root2:root3 D. F1:F2:F=root2:root3:root2

To solve this problem, let's set up the equations representing the given conditions:

Let F1 and F2 represent the magnitudes of the two forces, and let F represent the magnitude of the resultant force.

Condition 1: If F2 is doubled, F is also doubled.
Mathematically, this can be written as F = 2F2.

Condition 2: If F2 is reversed in direction, then F is also doubled.
Mathematically, this can be written as F = 2(-F2) = -2F2.

Now, let's use these equations to find the relationship between F1 and F2.

Since F2 is doubled in both cases, we can equate the equations for F:
2F2 = -2F2

This means that F2 = -F2, which implies that F2 = 0.

However, since F1 and F2 are two nonzero forces that have a resultant force, it is not possible for F2 to be zero.

Therefore, there is an inconsistency in the given conditions, and we cannot determine a valid relationship between F1 and F2 based on the information provided.

Hence, the answer would be E) Not enough information given to determine the relationship between F1 and F2.