Two forces each of 10N magnitude act on a body. If the forces are inclined at 30° and 60° with x- axis, then the x-component of their resultant is:
Correct answer: C. 13.66N
- A. 10N
- B. 1.366N
- C. 13.66N
- D. 136.6N
Explanation
To find the x-component of the resultant force when two forces of 10N magnitude are inclined at 30° and 60° with the x-axis, we need to find the x-components of each force individually and then sum them.The x-component of the first force is given by: F1x = 10N * cos(30°). The x-component of the second force is given by: F2x = 10N * cos(60°). Adding these components gives us the resultant x-component: Resultant x = F1x + F2x = (10N * cos(30°)) + (10N * cos(60°)) ≈ 13.66N. Therefore, the x-component of the resultant force is approximately 13.66N.
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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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