Question

Assertion :A hollow shaft is found to be stronger than a solid shaft made of same size and material. Reason: The torque required to produce a given twist in hollow cylinder is greater than that required to twist a solid cylinder of same size and material.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is D Both Assertion and Reason are incorrect

Give, Both shafts have equal size, means outer diameter of the shaft is same,

Hallow shaft

Inner diameter $=d_i$

Outer diameter $=d_0$

Ref. image 1

Solid shaft

Outer diameter $=d_0$

Ref. image 2

$\to$ If the size is same, There is more material used in the solid shaft, hence solid shaft will be stronger,

Assertion - wrong

$\to$ Torsional rigidity of solid shaft is more than the torsional rigidity of the hollow shaft

Hence more torque is required in the solid shaft to produce the same deformation.

Reason - wrong

Option - D