SSC JE Mechanical Engineering 2017 Set 4 Paper

Assume ‘T’ tension in string ${\mathit{R}}_{\mathit{a}}$ (Reaction at ball ‘a’), ${\mathit{R}}_{\mathit{b}}$ = reaction at ball ‘b’
All forces resolve in inclined plane in its perpendicular direction →.All forces in inclined direction should be in Equilibriums → ∑Fy = 0 (But inclined plane)
w cos 60° = T cos (90° – a)
∴ 2w sin 30° = T cos α .... (1)
w cos 60° = T sin α ......(2)
Dividing (2) by (1)
$\Rightarrow \frac{\mathit{T}\sin \mathit{\alpha }}{\mathit{T}\cos \mathit{\alpha }}=\frac{\mathit{w}\cos 60°}{2\mathit{w}\sin 30°}$
$\Rightarrow \tan \mathit{\alpha }=\frac{\sqrt{3}}{2}$
$\Rightarrow {\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)=\mathit{\alpha }$