Two forces of same magnitude F act on a body inclined at an angle of 90o, then the magnitude of their resultant is:
Correct answer: A. F√2
- A. F√2
- B. 2√2F
- C. 2F
- D. F/2
Explanation
The following is the solution: When two forces of the same magnitude (F) act on a body at an angle of 90 degrees, the magnitude of their resultant force (R) can be determined using the Pythagorean theorem. In this case, the forces are perpendicular to each other, forming a right-angled triangle. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (R) is equal to the sum of the squares of the other two sides (the magnitudes of the two forces, F). The Pythagorean theorem is given by: R2=F2+F2 Simplifying this equation: R2=2F2 Now, taking the square root of both sides: R=√2F2 R=F√2 So, the magnitude of the resultant force (R) is given by: R=F√2
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