Question

Resolve a weight of $10\, N$ in two directions which are parallel and perpendicular to a slope inclined at $ {{30}^{o}} $ to the horizontal.

• A. $ {{w}_{\bot }}=5\sqrt{3}N,\,{{w}_{||}}=5N $
• B. $ {{w}_{\bot }}=5N,\,{{w}_{||}}=5\sqrt{3}N $
• C. $ {{w}_{\bot }}=5\sqrt{3},\,{{w}_{||}}=0N $
• D. $ {{w}_{\bot }}=0N,\,{{w}_{||}}=5N $

Answer 1

Answer: (A)

Component perpendicular to the plane
$ {{w}_{\bot }}=w\,\cos {{30}^{o}} $
$ =10\times \frac{\sqrt{3}}{2} $
$ =5\sqrt{3}N $
and component parallel to the plane
$ {{w}_{||}}=w\sin {{30}^{o}} $
$ =10\times \frac{1}{2} = 5 \,N$