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Question

Assertion :A hollow shaft is found to be stronger than a solid shaft made of same 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
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Both Assertion and Reason are incorrect
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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
As both the shafts (cylinder) are made up of same material and have same size.
Mass of both the cylinders is same i.e M1=M2
ρ(πR2L)=ρ(π(r22r21)L)

R2=r22r21 ..........(1)
Torque required to twist the solid shaft τ=ηπϕR42L

Torque required to twist the hollow shaft τ=ηπϕ(r42r41)2L
ττ=r42r41R4=(r22r21)(r22+r21)R4

ττ=(r22+r21)R2 (using (1))
Equation (1) implies that R2<r22+r21
Thus τ>τ
Hence both assertion and the reason are correct and the reason is the correct explanation of assertion.

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