Question

A non-uniform rod AB of weight w is supported horizontally in a vertical plane by two light strings PA and QB as shown in the figure.G is the center of gravity of the rod. If PA and QB make angles 30∘ and 60∘ respectively with the vertical, the ratio AG/GB is

Answer 1

Explanation:

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Answer 2

Given :-

A non-uniform rod makes angle 30° and 60° with vertical.

${T}_{1}\:Cos{60}^{\circ}= {T}_{2}\:Sin{60}^{\circ}$

$\dfrac{{T}_{1}}{2} = \dfrac{\sqrt{3}{T}_{2}}{2}$

${T}_{1} = \sqrt{3}{T}_{2}$ ----(1)

√3T1/2 × AG = T2/2 × BG

AG/BG = T2/√3T1

But,

T2/T1 = 1/√3

Hence,

AG/BG = 1/3

AG:BG = 1:3