If a force of magnitude 8 N acts on a body in direction making an angle 30, its x and y components will be:
Correct answer: C. Fx = 4√3 and Fy = 4
- A. Fx = 4√3 and Fy = 8
- B. Fx = 8 and Fy = 4√3
- C. Fx = 4√3 and Fy = 4
- D. Fx = 8√3 and Fy = 4
Explanation
The x and y components of a force vector can be found using trigonometric functions: the x-component is given by Fx = F cosθ, and the y-component is given by Fy = F sinθ. For a force of 8 N at an angle of 30°, you calculate:Fx = 8 cos(30°) = 8 × (√3/2) = 4√3Fy = 8 sin(30°) = 8 × (1/2) = 4Thus, the correct components are Fx = 4√3 and Fy = 4. The other options either misuse the angle in calculations or incorrectly apply the trigonometric functions.
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About Rectangular Components
A vector is resolved into perpendicular horizontal and vertical components using trigonometric relations, usually as Ax = A cos θ and Ay = A sin θ when θ is measured from the horizontal. Questions involve signs in different quadrants, reconstructing a resultant from components, and using components to analyse equilibrium.
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