Two rods A and B of the same material and length have radii r1 and r2 respectively. When they are rigidly fixed at one end and twisted by the same torque applied at the other end, the ratio the angle of twist at the end of A the angle of twist at the end of B equals to

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r12r22

r13r23

r24r14

r14r24

answer is C.

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Detailed Solution

A rod of length L and radius r are fixed at one end and twisted by applying a torque τ at the other end, then the angle of twist θ is given by θ=2τLπr4ηwhere η is shear modulus of the material of the wire. As L, τ and η are same for both the wires∴ θ∝1r4 or θ1θ2=r2r14

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