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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 AssertionAs both the shafts (cylinder) are made up of same material and have same size.∴ Mass of both the cylinders is same i.e M1=M2ρ(πR2L)=ρ(π(r22−r21)L)⟹ R2=r22−r21 ..........(1)Torque required to twist the solid shaft τ=ηπϕR42LTorque required to twist the hollow shaft τ′=ηπϕ(r42−r41)2Lτ′τ=r42−r41R4=(r22−r21)(r22+r21)R4 ⟹ τ′τ=(r22+r21)R2 (using (1))Equation (1) implies that R2<r22+r21Thus τ′>τHence both assertion and the reason are correct and the reason is the correct explanation of assertion.

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