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Mechanical Properties of Solids — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMechanical Properties of Solids2 Marks
Question
Two cylinders A and B of radii r and 2r are soldered co-axially. The free end of A is clamped and the free end of B is twisted by an angle $\phi.$ Find twist at the junction taking the material of two cylinders to be same and of equal length.
✓

Answer

Let $\tau$ be the torque applied at the free end and $\phi'$ be the angle of twist at the junction. Then, $\tau=\frac{\pi\eta\text{r}^4(\phi'-0)}{2\text{l}}=\frac{\pi\eta(2\text{r})^4(\phi-\phi')}{2\text{l}}$ $\Rightarrow\phi'=16(\phi-\phi')\ \text{or}\ 17\phi'=16\phi\ \text{or }\phi'=\frac{16}{17}\phi.$

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