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 equation (1)and (2) , we get
` thete_1 = 8/9 theta `