Two forces of equal magnitude simultaneously act at a point. It is observed that the resultant force is equal in magnitude to the individual forces. Which of the following statements is/are correct? I. The angle between one of the individual forces and the resultant force is /3. II. The angle between the individual forces is 2 /3.
C. Both I and II
Let the two forces be F_1 and F_2 , and their resultant be R . Given that | F_1 | = | F_2 | = | R | = F. The magnitude of the resultant of two vectors is given by R^2 = F_1^2 + F_2^2 + 2F_1 F_2 , where is the angle between the two forces. Substituting the given values: F^2 = F^2 + F^2 + 2F^2 F^2 = 2F^2(1 + ) = - 1 2 = 2 3 Thus, the angle between the individual forces is 2 3 . Statement II is correct. Since the two forces are equal in magnitude, their resultant bisects the angle between them. Let be the angle between the resultant and one of the forces. = 2 = 1 2 ( 2 3 ) = 3 Thus, the angle between one of the individual forces and the resultant force is 3 . Statement I is also correct. Both statements I and II are correct.
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