GATE ME 2016 Set 1 — Question 18
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Strength of Materials → Beams & Columns → Torsion of Shafts
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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 and , and that the areas of the cross-sections are the same. and are the torsional rigidities of the bars on the left and right, respectively. The ratio is
Correct answer
(A) 1
Solution
Torsional rigidity for a hollow circular section is given by:
The area of the cross-section is .
Substituting into the expression for :
Given that the areas are the same ():
Since it is given that and , it follows that .
Therefore, , which means .
The area of the cross-section is .
Substituting into the expression for :
Given that the areas are the same ():
Since it is given that and , it follows that .
Therefore, , which means .
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