Two cylinders `A` and `B` of the same matieral have same length, their radii being in the ratio of `1:2` repectively. They are joined end to end as shown in figure. The upper end of `A` is rigidly fixed. The lower end of `B` is twised through an angle `theta`, the angle of twist of the cylinder `A` is:

Explanation

For cylinder `A, tau = (I eta r^(4))/(2l)`
For cylinder `B, tau = (pi eta (2r)^(4) (theta - theta'))/(2l)`
`therefore (pi eta r^(4))/(2l) theta' = pi eta (16 r^(4))/(2l) (theta- theta')`
`theta' = 16theta - 16 theta'`

`therefore theta' = (16)/(17) theta`