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

A rod of length 1 and radius .r. is joined to a rod of length 1/2 and

1.	A rod of length 1 and radius .r. is joined to a rod of length 1/2 and radius r/2 material. The free end of small rod is fixed to a rigid base and the free and of larger rod is given a twist of theta. The twist angle at the joint will be
Answer» Solution :`theta_(1)+theta_(2)= theta to (1)` we know that `theta PROP (L)/(r^(4))` `:.(theta_(1))/(theta_(2))=(l_(1))/(l_(2))xx(r_(2)^(4))/(r_(1^(4)))=(1//2)/(l)xx(r^(4))/((r//2)^(4))=8, (theta_(1))/(theta_(2))=8 to (2)` After solving equation (1) and (2), we get `theta_(1)=(8)/(9) theta`