Question

Calculate the twisting couple of a hollow cylinder. 

Answer 1

For a hollow cylinder of the same length land ofinner radius r₁ and outer radius r₂, Twisting couple of the cylinder

$$C=\int_{r_1}^{r_2}\frac{2\pi N\theta }{l}x^3dx\\ C=\frac{\pi N\theta}{2l}(r_2^4-r_1^4)$$