## Question

Two cylinders are twisted by the same external torque.If the ratios of their modulous of rigidity , radii & lengths are 1:2, 2:3 & 3:4 respectively. Then find the ratio of  angle of twist ??

Joshi sir comment

Let the angle rotated due to torque = θ and angle of twist (shear) = δ

then arc covered = rθ   (here r is radius)

now for twist of wire δ = rθ/l  (here l is length)

according to formula η = F/Aδ  and torque ζ = kFr    (here k is constant of proportion)

we get ζ = kηAδr

Use the formula and get the answer, you have to calculate ratio of δ's so k is not required