Torsion of Shafts MCQ with answer and solution

Concept

Torsional shear stress increases linearly with radial distance from the shaft axis.

Formula

τ = T r / J

Step-by-step solution

1. Use the torsion formula τ = T r / J. 2. τ is directly proportional to T (option D is true). 3. τ is directly proportional to r, the distance from the axis (option B is true). 4. τ is inversely proportional to J (option C is true). 5. τ is NOT inversely proportional to r, so option A is the answer.

Explanation

From τ = T r / J, shear stress is zero at the centre and maximum at the outer surface. It increases with distance from the axis, so it cannot be inversely proportional to that distance. Options B, C and D are all true statements.

Why the other options are wrong

B, C and D are all true from τ = T r / J. The question asks for the statement that is NOT true.

Shortcut

Read τ = T r / J directly: T and r are on top, J is at the bottom.

Common mistake

Missing the word 'not' in the question and choosing a true statement.