A rod of length 1 and radius .r. is joined to a rod of length `l//2` and radius `r//2` of same material. The free of small rod is fixed to a rigid base and the free end of larger rod is given a twist of `theta`. The twist angle at the point will be

Explanation

`theta_(1)+theta_(2)=theta to (1)`
we know that `theta prop (l)/(r^(4))`
`therefore (theta _(1))/(theta_(2)) =(l_(1))/(l_(2)) xx (r_(2)^(4))/(r_(1)^(4)) =(l//2)/(l)xx (r^(4))/((r//2)^(4)) =8`

`(theta_(1))/(theta_(2))=8" " to (2)`
After solving equations (1) and (2), we get
`theta_(1)=(8)/(9) theta`