A rod of length 1 and radius .r. is joinedto a rodof lengthl//2 and radiusr//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

A rod of length 1 and radius .r. is joinedto a rodof lengthl//2 and ra

1.	A rod of length 1 and radius .r. is joinedto a rodof lengthl//2 and radiusr//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
Answer» Solution :`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`