Question

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

• A. θ/ 4
• B. θ/ 2
• C. 5θ/ 6
• D. 8θ/ 9

Answer 1

Answer: (D)

8θ/ 9

Answer 2

If torque τ is applied at the free end of larger rod and twist θ is given to it then twist at joint is $\theta _ { 2 }$

$\tau = \frac { \pi \eta r ^ { 4 } \left( \theta - \theta _ { 1 } \right) } { 2 l } = \frac { \pi \eta \left( \frac { r } { 2 } \right) ^ { 4 } \left( \theta _ { 1 } - \theta _ { 2 } \right) } { 2 ( l / 2 ) }$⇒$\left( \theta - \theta _ { 1 } \right) = \frac { \left( \theta _ { 1 } - 0 \right) } { 8 }$

⇒ $8 \theta - 8 \theta _ { 1 } = \theta _ { 1 }$ $\theta _ { 1 } = \frac { 8 \theta } { 9 }$.