Two rod A and B of the same material and dame length have radii `r_(1) and r_(2)` respectively. When they are rigidly fixed at one end and twisted by the same couple applied at the other end, find the ratio of the angles of twist at the ends of A and B.

Explanation

If a wire of length l, and radius r is fixed at one end and a torque `tau` is applied at the other end produces angle of twist `theta` in the wire, then
`tau = (pi G r^(4)theta)/(2l) or theta = (2 tau l)/(pi G r^(4))`
i.e., `theta prop 1/(r^4) so (theta_(1))/(theta_2) = (r_(2)^(4))/(r_(1)^(4))`.