ratio of j2 and j1

Question

The cross sections of two hollow bars made of the same material are concentric circles as shown in the figure. It is given that r₃ > r₁ and r₄ > r₂, and that the areas of the cross-sections are the same.

J₁ and J₂ are the torsional rigidities of the bars on the left and right, respectively. The ratio J₂/J₁ is 

 

 

(a) >1                  

(b) <0.5

(c) = 1

(d) between 0.5 and 1

 

Answer 1

Given two hollow bars made of the same material,