Question

The twisting couple per unit twist for a solid cylinder of radius $4.9cm$ is $0.1N/m$. The twisting couple per unit twist for a hollow cylinder of same material with outer and inner radii of $5cm$ and $4cm$ respectively, will be

• A. $0.64N/m$
• B. $0.64\times {10}^{-1}N/m$
• C. $0.64\times {10}^{-2}N/m$
• D. $0.64\times {10}^{-3}N/m$

Answer 1

Answer: (B)

$0.64\times {10}^{-1}N/m$

Radius of solid cylinder $r_1=4.9cm$

Outer radius of Hollow cylinder $R_2=5cm$

Inner radius of Hollow cylinder $r_2=4cm$

Twisting Couple $G=C\theta$ where $C=\frac{\pi \eta r^4}{2l}$

$\therefore$ Twisting couple per unit twist = $\frac{G}{\theta }=C$

Given: ${\left(G/\theta \right)}_1=0.1N/m$

$\frac{G}{\theta }$ is proportional to $r^4$.

Hence,

$\frac{{\left(G/\theta \right)}_1}{{\left(G/\theta \right)}_2}=\frac{{r_1}^2}{{R_2}^2-{r_2}^2}$

Substituting the values in the above equation gives,

${\left(G/\theta \right)}_2=0.64\times {10}^{-1}N/m$